This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 7 Integrals – Quiz 3 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 3 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $\int_2^5\left(x^3+3\right)dx$ A) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3i}{n}$. B) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{1}{n}$. C) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$. D) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$. Show Answer Correct Answer: C) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$. 2. $\int_0^{\frac{\pi}{2}}\int_0^1rdrd\theta$ A) 1. B) $\frac{\pi}{2}$. C) $\frac{\pi}{4}$. D) 0. Show Answer Correct Answer: C) $\frac{\pi}{4}$. 3. Calculate the average value of the function $f(x) = x^2$ $[0, 2]$ A) $\frac{4}{3}$. B) 3. C) $\frac{2}{3}$. D) 2. Show Answer Correct Answer: A) $\frac{4}{3}$. 4. What is the antiderivative of $f(x) = \frac{1}{x}$ A) $\ln|x| + C$. B) $x\ln(x)-x + C$. C) $\frac{1}{2}x^2 + C$. D) $e^x + C$. Show Answer Correct Answer: A) $\ln|x| + C$. 5. Evaluate the indefinite integral. $\int_{ }^{ }\left(2x+2x^{-3}-6x^{-4}\right)dx$ A) $2x^2+2x^{-2}-6x^{-3}+C$. B) $x-x^{-3}+2x^4+C$. C) $x^2-x^{-2}+2x^{-3}+C$. D) $-2x+C$. Show Answer Correct Answer: C) $x^2-x^{-2}+2x^{-3}+C$. 6. $\int_0^3g\left(x\right)dx=-5$ $\int_3^02g\left(x\right)dx=$ A) $-7$. B) $10$. C) $-10$. D) $-\frac{5}{2}$. Show Answer Correct Answer: B) $10$. 7. $\int_0^{\pi/2}\int_0^{\pi/2}\cos\theta\cos\varphi d\theta d\varphi$ A) 1. B) 0. C) $\pi$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: A) 1. 8. Which of the following is the solution to the differential equation dy/dx = e$^{y+x}$ with the initial condition y(0) =-ln 4? A) Y =-x-ln 4. B) Xy = x-ln 4. C) Y =-ln(-e$^{x}$ + 5). D) Y =-ln(e$^{x}$ + 3). E) Y = ln(e$^{x}$ + 3). Show Answer Correct Answer: C) Y =-ln(-e$^{x}$ + 5). 9. The integration of f(x)= 1/tan(x) dx is:HINT:What is 1/tan(x) the same as? A) -ln Icos(x)I + C. B) Ln Isin(x)I +C. C) -ln Isin(x)I +C. D) Sec$^{2}$ (x) + C. Show Answer Correct Answer: B) Ln Isin(x)I +C. 10. The percentage of error using the trapezoidal rule with 3 strips for $\int_0^3x\left(3-x\right)dx$ A) 10%. B) 9%. C) 11%. D) 12%. Show Answer Correct Answer: C) 11%. 11. $\int_{ }^{ }\\frac{1}{a^2+x^2}dx=$ A) $\frac{1}{a}\arcsin\\frac{x}{a}+C$. B) $\frac{1}{a}\arctan\\frac{x}{a}+C$. C) $\arctan\\frac{x}{a}+C$. D) $\arcsin\\frac{x}{a}+C$. Show Answer Correct Answer: B) $\frac{1}{a}\arctan\\frac{x}{a}+C$. 12. In $\int_0^1\int_0^{1-z}\int_0^{1-y-z}xyzdxdydz$ A) 0 to 1-z. B) 0 to 1-y-z. C) 0 to 1. D) 1 to 1-y-z. Show Answer Correct Answer: B) 0 to 1-y-z. 13. $\int_{ }^{ }-24x^5\\dx$ A) $-6x^4+C$. B) $-4x^5+C$. C) $-4x^6+C$. D) $-24x^6+C$. Show Answer Correct Answer: C) $-4x^6+C$. 14. $\int_0^{\\pi}\sin\left(x\right)\\dx$ A) 2. B) 1. C) 0. D) -1. E) -2. Show Answer Correct Answer: A) 2. 15. Find the average value of $f\left(x\right)=6-2x$ $\left[-1, 4\right]$ A) 3. B) 3.2. C) 10. D) 15. Show Answer Correct Answer: A) 3. 16. Single integral gives the area under a curve. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 17. Evaluate:$\int_4^{\infty}\frac{-2x}{\left(9-x^2\right)^{\frac{1}{3}}}dx$ A) $\frac{3}{2}\left(9^{\frac{2}{3}}+7^{\frac{2}{3}}\right)$. B) $9^{\frac{2}{3}}+7^{\frac{2}{3}}$. C) $\frac{3}{2}\cdot7^{\frac{2}{3}}$. D) Diverges. E) $7^{\frac{2}{3}}$. Show Answer Correct Answer: D) Diverges. 18. $\int\int\left(y-z\right)dxdy$ A) $\frac{1}{2}xy^2-xyz+C$. B) $\frac{1}{2}xy^2-x^2yz+C$. C) $\frac{1}{2}x^2y^{ }-xyz+C$. D) $\frac{1}{2}xy^2+xyz+C$. Show Answer Correct Answer: A) $\frac{1}{2}xy^2-xyz+C$. 19. $\int_{ }^{ }\\dy$ A) $1+C$. B) $\frac{1}{2}y^2+C$. C) $x+C$. D) $y+C$. Show Answer Correct Answer: D) $y+C$. 20. Integral of $\frac{1}{e^x+e^{-x}}$ A) $\tan^{-1}\left(e^x\right)+C$. B) $\tan^{-1}\left(e^{-x}\right)+C$. C) $\log\left(e^x+e^{-x}\right)+C$. D) $\log\left(e^x-e^{-x}\right)+C$. Show Answer Correct Answer: A) $\tan^{-1}\left(e^x\right)+C$. 21. $\int_{-a}^a\left(2\sin2x\right)dx$ A) -2a. B) 2a. C) -a. D) 0. Show Answer Correct Answer: D) 0. 22. $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{5i}{n}\right)^2+\frac{5i}{n}+1\right]\frac{5}{n}$ A) $\int_5^6\left(x^2+x+1\right)dx$. B) $\int_0^1\left(\left(5x\right)^2+5x+1\right)dx$. C) $\int_0^5\left(x^2+x+1\right)dx$. D) $\int_0^{10}\left(\frac{x^2}{2}+\frac{x}{2}+1\right)dx$. Show Answer Correct Answer: C) $\int_0^5\left(x^2+x+1\right)dx$. 23. What is the answer to page 7, #1? A) D. B) C. C) B. D) A. E) E. Show Answer Correct Answer: C) B. 24. $\int_{ }^{ }9\sin\left(3x\right)dx$ A) $-3\cos\left(3x\right)+C$. B) $-27\cos\left(3x\right)+C$. C) $27\cos\left(3x\right)+C$. D) $3\cos\left(3x\right)+C$. Show Answer Correct Answer: A) $-3\cos\left(3x\right)+C$. 25. $\int_1^3\left(4-2x\right)dx=$ A) $-0.4$. B) $-\frac{5}{2}$. C) 6. D) $\frac{2}{5}$. E) 0. Show Answer Correct Answer: E) 0. 26. How do you get from the first derivative the the original function? A) Differentiate. B) Integrate. C) All the above. D) None of the above. Show Answer Correct Answer: B) Integrate. 27. Evaluate the definite integral $\int_1^e \frac{1}{x} \, dx$ A) E. B) 1. C) $e-1$. D) $\ln(e)$. Show Answer Correct Answer: B) 1. 28. $\int\int\int\left(x^2+y^2+z^2\right)dxdydz$ A) $\frac{1}{3}xyz\left(x^2y^2z+xy^2z^2+x^2yz^2\right)+C$. B) $\frac{1}{3}xyz\left(x^2+y^2+z^2\right)+C$. C) $3xyz\left(x^2yz+xy^2z+xyz^2\right)+C$. D) $xyz\left(x^2yz+xy^2z+xyz^2\right)+C$. Show Answer Correct Answer: B) $\frac{1}{3}xyz\left(x^2+y^2+z^2\right)+C$. 29. $\int\frac{2x}{x^2+1}dx$ A) $\ln\left|2x\right|$. B) $\frac{1}{2x}$. C) $\ln\left|x^2+1\right|$. D) $\frac{1}{\left(x^2+1\right)^2}$. Show Answer Correct Answer: C) $\ln\left|x^2+1\right|$. 30. A ball is thrown vertically upward from ground level with an initial velocity of 40 m/sec. (note:$a\left(t\right)=-9.8\\frac{m}{\sec^2}^{ }$ A) 4.08 sec. B) 2.04 sec. C) All the above. D) None of the above. Show Answer Correct Answer: B) 2.04 sec. 31. $\int_{ }^{ }5x^{-4}dx$ A) $-x^{-5}+c$. B) $-\frac{5}{3}x^3+c$. C) $c-\frac{5}{3x^3}$. D) $\frac{5}{3x^3}+c$. Show Answer Correct Answer: C) $c-\frac{5}{3x^3}$. 32. A solid S is bounded by the planes $x+2y+z=2$ $x=2y$ $x=0$ $z=0$ A) Upper surface:$z=2-x-2y$ $z=0$. B) Upper surface:$z=2-x-2y$ $\left[0, \frac{x}{2}\right]$. C) Interval for x:$\left[0, 1\right]$ $\left[\frac{x}{2}, 1-\frac{x}{2}\right]$. D) None of the above. Show Answer Correct Answer: B) Upper surface:$z=2-x-2y$ $\left[0, \frac{x}{2}\right]$. 33. When applying calculus. The second derivative helps find ..... A) The distance traveled by an object. B) The velocity of a particle at any given point. C) Acceleration of an object at any given time. D) None of the above. Show Answer Correct Answer: C) Acceleration of an object at any given time. 34. $\int_2^4g\left(x\right)dx=12$ $\int_2^4\left(mg\left(x\right)-2x\right)dx=15.$ $m=?$ A) $-\frac{9}{2}$. B) $\frac{9}{4}$. C) $4$. D) $2.5$. Show Answer Correct Answer: B) $\frac{9}{4}$. 35. The position function x(t)=7t$^{2}$-18t-7 is given. What is the velocity function? A) V(t)=18t-14. B) V(t)=18t+14. C) V(t)=14t-18. D) V(t)=14t+18. Show Answer Correct Answer: C) V(t)=14t-18. 36. Evaluate the indefinite integral. $\int_{ }^{ }\left(16x^3+5-6x^{-3}\right)dx$ A) $16x^4+5x-6x^{-2}+C$. B) $4x^3+5+3x^{-3}+C$. C) $15x+C$. D) $4x^4+5x+3x^{-2}+c$. Show Answer Correct Answer: D) $4x^4+5x+3x^{-2}+c$. 37. $3\int_{ }^{ }\left(\sin\left(x\right)+x^2+e^x\right)dx$ A) $\cos\left(3x\right)+3x^3+3e^x+C$. B) $3\cos\left(x\right)+\frac{x^3}{3}+e^x+C$. C) $3\cos\left(3x\right)+\frac{x^3}{3}+3e^x+C$. D) $-3\cos\left(x\right)+x^3+3e^x+C$. Show Answer Correct Answer: D) $-3\cos\left(x\right)+x^3+3e^x+C$. 38. Evaluate $\int0dx$ A) $c$. B) C Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $c$. 39. Calculate the following integral:$\int_3^0\left(x+2\right)dx$ A) 21/2. B) 11. C) -21/2. D) -10. Show Answer Correct Answer: C) -21/2. 40. The antiderivative of $f\left(x\right)=\frac{15}{x^4}+\frac{8}{x^3}$ A) $-\frac{5}{x^3}-\frac{4}{x^2}+C$. B) $\frac{3}{x^5}+\frac{2}{x^4}+C$. C) $\frac{60}{x^3}+\frac{24}{x^2}+C$. D) $-\frac{15}{x^3}-\frac{8}{x^2}+C$. Show Answer Correct Answer: A) $-\frac{5}{x^3}-\frac{4}{x^2}+C$. 41. $\int_{ }^{ }a^xdx$ A) $\frac{1}{\ln\left(a\right)}a^x+C$. B) $\ln\left(a\right)a^x+C$. C) $\frac{a^{\left(x+1\right)}}{x+1}+C$. D) $\log_a\left(x\right)a^x+C$. Show Answer Correct Answer: A) $\frac{1}{\ln\left(a\right)}a^x+C$. 42. The acceleration function is the first derivative of ..... A) Velocity. B) Particle motion. C) Position. D) Calculus. Show Answer Correct Answer: A) Velocity. 43. $\int_{-4}^4\left|x+2\right|dx=$ A) 10. B) Not possible. C) 40. D) 20. Show Answer Correct Answer: D) 20. 44. $\int6x\left(x+2\right)dx$ A) $2x^3+6x^2+c$. B) 2x3+6x2+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $2x^3+6x^2+c$. 45. Evaluate the following definite integral via u-substitution $\int_0^1\frac{6x}{\left(3x^2+1\right)^2}dx$ A) $-\frac{5}{4}$. B) $\frac{65}{192}$. C) $\frac{21}{64}$. D) $\frac{3}{4}$. Show Answer Correct Answer: D) $\frac{3}{4}$. 46. What is the antiderivative of $f(x) = 3x^2$ A) $\frac{3}{2}x^3 + C$. B) $\frac{3}{2}x^3$. C) $x^3$. D) $x^3 + C$. Show Answer Correct Answer: A) $\frac{3}{2}x^3 + C$. 47. Find the average value of $f\left(x\right)=\sqrt{2x-1}$ $x=\frac{1}{2}$ $x=1$ A) 4/3. B) 2/3. C) 1/3. D) 1/6. Show Answer Correct Answer: B) 2/3. 48. The population of a town grows at a rate of r(t) people per year (where t is time in years). What does $\int_2^4r\left(t\right)dt$ A) The time it took for the town to grow from a population of 2 people to a population of 4 people. B) The number of people in the town on the fourth year. C) The average rate at which the population grew between the second and the fourth year. D) The change in the number of people between the second and the fourth year. Show Answer Correct Answer: D) The change in the number of people between the second and the fourth year. 49. $\int\frac{1}{2x}dx=$ A) $\ln\left|2x\right|+c$. B) $\frac{1}{2}\ln\left|2x\right|+c$. C) $2\ln\left|x\right|+c$. D) $2\ln\left|2x\right|+c$. Show Answer Correct Answer: B) $\frac{1}{2}\ln\left|2x\right|+c$. 50. Evaluate the definite integral $\int_{-1}^1 (3x^3-x) \, dx$ A) 4. B) 2. C) 0. D) -2. Show Answer Correct Answer: C) 0. 51. $\int_{ }^{ }\\frac{1}{\sqrt{a^2-x^2}}dx=$ A) $\arcsin\\frac{x}{a}+C$. B) $\frac{1}{a}\arctan\\frac{x}{a}+C$. C) $\frac{1}{a}\arcsin\\frac{x}{a}+C$. D) $\arctan\\frac{x}{a}+C$. Show Answer Correct Answer: A) $\arcsin\\frac{x}{a}+C$. 52. $\int_1^2\left(4-x\right)dx=$ A) 2.5. B) $\frac{2}{5}$. C) $-0.4$. D) $-\frac{5}{2}$. Show Answer Correct Answer: A) 2.5. 53. $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[2+\sqrt{3+\frac{4i}{n}}\right]\frac{4}{n}$ A) $\int_3^7\left(2+\sqrt{x}\right)dx$. B) $\int_0^4\left(2+\sqrt{x}\right)dx$. C) $\int_3^7\left(2+\sqrt{3+x}\right)dx$. D) $\int_3^7\left(2x+\sqrt{x}\right)dx$. Show Answer Correct Answer: A) $\int_3^7\left(2+\sqrt{x}\right)dx$. 54. $\int_1^2\int_0^2e^xdydx$ A) $e^2$. B) $e^2-e$. C) $e^2-1$. D) $2\left(e^2-e\right)$. Show Answer Correct Answer: D) $2\left(e^2-e\right)$. 55. $5\int_{ }^{ }\pi^xdx$ A) $\frac{5\pi^x}{\ln\left(\pi\right)}+C$. B) $\frac{5\pi}{\ln\left(x\right)}+C$. C) $\frac{5\pi^x}{\ln\left(5\right)}+C$. D) $\frac{5\pi^{\left(x+1\right)}}{x+1}+C$. Show Answer Correct Answer: A) $\frac{5\pi^x}{\ln\left(\pi\right)}+C$. 56. What is the antiderivative of $f(x) =\cos(x)$ A) $\tan(x) + C$. B) $-\tan(x) + C$. C) $-\sin(x) + C$. D) $\sin(x) + C$. Show Answer Correct Answer: D) $\sin(x) + C$. 57. Evaluate $\int\left(6\sqrt{x}-1\right)dx$ A) $4x^{\frac{3}{2}}-x+c$. B) 4x23-x+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $4x^{\frac{3}{2}}-x+c$. 58. How many Harry Potter movies are there? A) 9. B) 7. C) 5. D) 8. Show Answer Correct Answer: D) 8. 59. $\int_{ }^{ }\left(x+1\right)\left(2x-3\right)dx$ A) $\frac{2}{3}x^3-\frac{x^2}{2}-3x+c$. B) $\left(\frac{x^2}{2}+x\right)\left(x^2-3x\right)+c$. C) $\frac{2}{3}x^3-\frac{x^2}{2}+3x+c$. D) $\frac{2}{3}x^2-\frac{x}{2}-3+c$. Show Answer Correct Answer: A) $\frac{2}{3}x^3-\frac{x^2}{2}-3x+c$. 60. $\int\int x^2dydx$ A) $x^3y^3+C$. B) $\frac{1}{3}x^3y+C$. C) $\frac{1}{3}xy^3+C$. D) $\frac{1}{3}x^3y^3+C$. Show Answer Correct Answer: B) $\frac{1}{3}x^3y+C$. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 7 Integrals Quiz 1Class 12 Mathematics Chapter 7 Integrals Quiz 2Class 12 Mathematics Chapter 7 Integrals Quiz 4Class 12 Mathematics Chapter 7 Integrals Quiz 5Class 12 Mathematics Chapter 1 Relations And Functions QuizClass 12 Mathematics Chapter 10 Vector Algebra QuizClass 12 Mathematics Chapter 11 Three Dimensional Geometry QuizClass 12 Mathematics Chapter 12 Linear Programming Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books