This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 7 Integrals – Quiz 4 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 4 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Given F'(x) = x + 2 and F(0) = 3, find the particular solution for F(x). A) X$^{2}$ + 2x + 6. B) X$^{2}$ + 3. C) 1/2 x$^{2}$ + 2x + 3. D) 1/2 x$^{2}$ + 2x + 6. Show Answer Correct Answer: C) 1/2 x$^{2}$ + 2x + 3. 2. $\int_{ }^{ }4dx$ A) $4$. B) $2x^2+c$. C) $4x+c$. D) $0$. Show Answer Correct Answer: C) $4x+c$. 3. Let $A\left(x\right)=\int_0^x\sqrt{9-x^2}dx$ $A'\left(0\right)$ A) 0. B) -3. C) 9. D) 3. Show Answer Correct Answer: D) 3. 4. A particle moves along an axis so that at any time t>0, its velocity is given by v(t)=4-6t$^{2}$. If the particle is at position p=7 at t=1, what is the position of the particle at t=2? A) -5. B) 3. C) -3. D) -10. Show Answer Correct Answer: C) -3. 5. Evaluate $\int5x^4dx$ A) $x^5+c$. B) X5+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $x^5+c$. 6. What is the answer to page 4, #5? A) C. B) E. C) A. D) B. E) D. Show Answer Correct Answer: D) B. 7. Calculate the average value of the function $f(x) = 4x$ $[1, 3]$ A) 6. B) 10. C) 8. D) 4. Show Answer Correct Answer: C) 8. 8. $\int_1^3\left(2-\frac{3}{x^2}\right)dx=$ A) $0.5$. B) $-\frac{1}{2}$. C) 2. D) $-2$. Show Answer Correct Answer: C) 2. 9. $\int\\frac{-2x}{\sqrt[]{-x^4+2x^2}}dx$ A) $\sqrt[]{-x^4+2x^2}+c$. B) $\sin^{-1}\left(1-x^2\right)+c$. C) $\cos^{-1}\left(x^2-1\right)+c$. D) $\csc^{-1}\left(x^2\right)+c$. Show Answer Correct Answer: C) $\cos^{-1}\left(x^2-1\right)+c$. 10. $\int_{ }^{ }\csc^2\left(x\right)dx$ A) $\cot\left(x\right)+C$. B) $-\csc\left(x\right)+C$. C) $\frac{\csc^3\left(x\right)}{3}+C$. D) $-\cot\left(x\right)+C$. Show Answer Correct Answer: D) $-\cot\left(x\right)+C$. 11. Find $\int(x^2+x+1)dx$ A) $x^3+x^2+x$. B) $\frac{1}{3}x^3+\frac{1}{2}x^2+x+c$. C) $x^3+x^2+x+c$. D) $\frac{1}{3}x^3+\frac{1}{2}x^2+x$. Show Answer Correct Answer: B) $\frac{1}{3}x^3+\frac{1}{2}x^2+x+c$. 12. For a function that is strictly decreasing, a right hand Riemann Sum is which of the following: A) Unable to Determine. B) Overestimate. C) Underestimate. D) Exact Solution. Show Answer Correct Answer: C) Underestimate. 13. Find the particular solution:f'(x) = 6x when f(-3) = 20 A) F(x)=3x$^{2}$-7. B) F(x)=3x$^{2}$ + 7. C) F(x)=3x$^{2}$ + 47. D) F(x)=3x-7. Show Answer Correct Answer: A) F(x)=3x$^{2}$-7. 14. $\int_0^2\int_0^{\infty}e^{-x}dxdy$ A) $e^2-1$. B) 1. C) 2. D) $e^{-2}-1$. Show Answer Correct Answer: C) 2. 15. Use $a\left(t\right)=-32\\frac{ft}{\sec^2}$ A) $1.75$. B) 1.75 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $1.75$. 16. $\int_1^3\left(x^2+1\right)dx$ A) $\frac{30}{3}$. B) $\frac{31}{3}$. C) $\frac{32}{3}$. D) $\frac{29}{3}$. Show Answer Correct Answer: C) $\frac{32}{3}$. 17. Evaluate $\int\sqrt{x}dx$ A) $\frac{2}{3}x^{\frac{3}{2}}+C$. B) $x^{\frac{1}{2}}+C$. C) $x^{\frac{3}{2}}+C$. D) $\frac{1}{2}x^{-\frac{1}{2}}+C$. Show Answer Correct Answer: A) $\frac{2}{3}x^{\frac{3}{2}}+C$. 18. Given the demand function, $D(x)=9-x^2$ $S(x)=x^2+1$ A) RM5.33. B) 5. C) 2. D) RM1.33. Show Answer Correct Answer: A) RM5.33. 19. Which country is NOT in South America? A) Mexico. B) Peru. C) Brazil. D) Uruguay. Show Answer Correct Answer: A) Mexico. 20. The velocity of a particle moving along an axis is given by v(t)=2-t$^{2}$ for t>0, what is the average velocity of the particle from t=1 to t=3? A) -4. B) -7/3. C) 8/3. D) -3. Show Answer Correct Answer: B) -7/3. 21. What does c represent in an indefinite integral? A) A variable. B) A coefficient. C) A constant. D) None of these. Show Answer Correct Answer: C) A constant. 22. Find the particular solution:If F'(x) = 4x and F(1) = 6, then F(2) = A) 9. B) 12. C) 6. D) 8. Show Answer Correct Answer: B) 12. 23. Evaluate $\int_{-\infty}^{\infty}\frac{x}{\left(x^2+3\right)^2}dx$ A) -2. B) 0. C) 4. D) Diverges. Show Answer Correct Answer: B) 0. 24. $\int_{ }^{ }\left(\sin^2\left(x\right)+\cos^2\left(x\right)\right)dx$ A) $x+C$. B) $\frac{\sin^3\left(x\right)}{3}-\frac{\cos^3\left(x\right)}{3}+C$. C) $\frac{\sin^3\left(x\right)}{3}+\frac{\cos^3\left(x\right)}{3}+C$. D) Can not integrate. Show Answer Correct Answer: A) $x+C$. 25. Integrate $\int\left(-20x^3-6x^{-3}\right)dx$ A) $-5x^3+\frac{3}{x^3}+C$. B) $-20x^4+\frac{3}{2}+C$. C) $-5x^4+\frac{3}{x^2}+C$. D) $-20x^4-\frac{6}{x^2}+C$. Show Answer Correct Answer: C) $-5x^4+\frac{3}{x^2}+C$. 26. Find the area indicated by the following integral:$\int_0^{12}\left(4x\right)dx$ A) 288. B) 0. C) 48. D) 144. E) 72. Show Answer Correct Answer: A) 288. 27. Evaluate:$\int_0^3\frac{3}{x}dx$ A) Divergent. B) 1. C) $e^3$. D) $3e$. Show Answer Correct Answer: A) Divergent. 28. The correct formula for Trapezoidal Rule of the definite integral $\int_a^bydx$ $y=f\left(x\right)$ A) $\frac{b-a}{2n}\left[y_0+y_n+2\left(y_1+y_2+ y_{n-1}\right)\right]$. B) $\frac{b-a}{n}\left[y_0+y_n+\left(y_1+y_2+ +y_{n-1}\right)\right]$. C) $\frac{b-a}{n}\left[y_0+y_n+2\left(y_1+y_2+ +y_{n-1}\right)\right]$. D) $\frac{b-a}{2n}\left[y_0+y_n+y_1+y_2+ +y_{n-1}\right]$. Show Answer Correct Answer: A) $\frac{b-a}{2n}\left[y_0+y_n+2\left(y_1+y_2+ y_{n-1}\right)\right]$. 29. Find the area under a curve $5x^4+3x+7$ A) 1200. B) 1/12. C) 1134. D) 1076. Show Answer Correct Answer: D) 1076. 30. $\int\frac{3}{x+2}dx$ A) $3\ln\left|x\right|+c$. B) $\ln\left|x+2\right|+c$. C) $3\left(x+2\right)+c$. D) $3\ln\left|x+2\right|+c$. Show Answer Correct Answer: D) $3\ln\left|x+2\right|+c$. 31. Find the expression that would represent the area under the curve $f\left(x\right)=3x^2-2x$ A) $\int_1^5\left(x^3-x^2\right)dx$. B) $\int_5^1\left(3x^2-2x\right)dx$. C) $\int_1^5\left(3x^2-2x\right)dx$. D) $\int_1^5\left(6x-2\right)dx$. Show Answer Correct Answer: C) $\int_1^5\left(3x^2-2x\right)dx$. 32. The demand function, $D(x)=10-x^2$ $S\left(x\right)=x^2+x$ A) RM5.33. B) $x=2, y=6$. C) $\left(-\frac{5}{2}, 6\right)$. D) $\left(2, 6\right)$. Show Answer Correct Answer: D) $\left(2, 6\right)$. 33. In $\int_0^2\int_0^{x^{ }}f(x, y)dydx$ A) 2 to x. B) 0 to y. C) 0 to 2. D) 0 to x. Show Answer Correct Answer: D) 0 to x. 34. The integration of f(x)= sin(x)/cos(x) dx is:HINT:QUOTIENT IDENTITY! A) -ln Isin(x)I +C. B) Ln Isin(x)I +C. C) Sec$^{2}$ (x) + C. D) -ln Icos(x)I + C. Show Answer Correct Answer: D) -ln Icos(x)I + C. 35. What is the antiderivative of $f(x) = e^x$ A) $xe^x + C$. B) $e^x + C$. C) $\ln(x) + C$. D) $x\ln(x)-x + C$. Show Answer Correct Answer: B) $e^x + C$. 36. If $\int_2^5f\left(x\right)dx=5$ $\int_4^5f\left(x\right)dx=\pi$ $\int_5^5f\left(x\right)dx=?$ A) $0$. B) 0 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $0$. 37. $\int_{ }^{ }3\cos\left(x\right)dx$ A) $3\sin\left(x\right)+C$. B) $3x\cos\left(x\right)+C$. C) $3\sin^2\left(x\right)+C$. D) $-3\sin\left(x\right)+C$. Show Answer Correct Answer: A) $3\sin\left(x\right)+C$. 38. What is the answer to page 7, #3? A) D. B) C. C) A. D) B. E) E. Show Answer Correct Answer: A) D. 39. If a function is strictly increasing then using a left-hand Riemann Sum will produce an: A) Over-estimate. B) Exact Solution. C) Under-estimate. D) Undefined Value. Show Answer Correct Answer: C) Under-estimate. 40. If $\int_2^{10}f\left(x\right)dx=-6$ $\int_2^{10}3f\left(x\right)dx$ A) -9. B) -3. C) 18. D) -18. Show Answer Correct Answer: D) -18. 41. $\int_1^2x\cdot e^{\left(1-x^2\right)}+\frac{1}{2x+1}dx$ A) $\ln\left(3\right)+\ln\left(5\right)-\frac{1}{2}e^{-3}$. B) $\ln\frac{5}{3}-\frac{e^3}{2}+\frac{1}{2}$. C) $\frac{e^{-3}}{2}-\ln\left(\frac{3}{2}\right)+\ln\left(5\right)$. D) $\frac{1}{2}\left(1-\ln\left(3\right)+\ln\left(5\right)-e^{-3}\right)$. Show Answer Correct Answer: D) $\frac{1}{2}\left(1-\ln\left(3\right)+\ln\left(5\right)-e^{-3}\right)$. 42. $5\int_{ }^{ }x^4dx$ A) $5x^5+C$. B) $15x^3+C$. C) $x^5+C$. D) $\frac{x^5}{5}+C$. Show Answer Correct Answer: C) $x^5+C$. 43. If f'(x) = 4x and f(1) = 6, then f(2) = A) 8. B) 9. C) 6. D) 12. Show Answer Correct Answer: D) 12. 44. $\int\int\int\left(2x-3y+4z\right)dxdydz$ A) $xyz\left(x-\frac{3}{2}y+2z\right)+C$. B) $xyz\left(x-3y+2z\right)+C$. C) $xyz\left(x+\frac{3}{2}y+2z\right)+C$. D) $xyz\left(x+3y+2z\right)+C$. Show Answer Correct Answer: A) $xyz\left(x-\frac{3}{2}y+2z\right)+C$. 45. Evaluate the definite integral $\int_0^3\left(3x^2\right)dx$ A) 27. B) 21. C) 23. D) 25. Show Answer Correct Answer: A) 27. 46. What is the value of the definite integral $\int_2^4\\ln\left(x\right)dx$ A) $4\ln\left(2\right)-2$. B) $10\ln\left(2\right)-2$. C) $6\ln\left(2\right)+2$. D) $6\ln\left(2\right)-2$. Show Answer Correct Answer: D) $6\ln\left(2\right)-2$. 47. $\int_{ }^{ }\sin\left(2x+3\right)dx$ A) $\cos\left(2x+3\right)+C$. B) $-\frac{1}{2}\cos\left(2x+3\right)+C$. C) $-\frac{1}{5}\cos\left(2x+3\right)+C$. D) $\frac{1}{2}\cos\left(2x+3\right)+C$. E) $-\cos\left(2x+3\right)+C$. Show Answer Correct Answer: B) $-\frac{1}{2}\cos\left(2x+3\right)+C$. 48. $\int_0^2\int_0^2dxdy$ A) 2. B) 4. C) 1. D) 3. Show Answer Correct Answer: B) 4. 49. The integration of f(x)= sin(x)/cos(x) dx is: 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: A) -ln Icos(x)I + C. 50. For a function that is strictly decreasing, a right hand Riemann Sum (Right Endpoint Approximation) is which of the following: A) Overestimate. B) Exact Solution. C) Unable to Determine. D) Underestimate. Show Answer Correct Answer: D) Underestimate. 51. The integration of f(x)= 1/tan(x) dx is: A) Ln Isin(x)I +C. B) -ln Isin(x)I +C. C) Sec$^{2}$ (x) + C. D) -ln Icos(x)I + C. Show Answer Correct Answer: A) Ln Isin(x)I +C. 52. $\int_1^2\frac{1}{\left(4x-3\right)^2}dx=$ A) $1.5$. B) 15. C) $-\frac{1}{5}$. D) 0.2. Show Answer Correct Answer: D) 0.2. 53. Choose the correct next step $\int_1^36x^5dx=$ A) $\left[x^6\right]_1^3$. B) $3^6-1^6$. C) $\left[6x^5\right]_1^3$. D) $6\left(3\right)^5-6\left(1\right)^5$. Show Answer Correct Answer: A) $\left[x^6\right]_1^3$. 54. What is the value of the definite integral $\int_0^{\frac{\pi}{2}}\\cos\left(x\right)dx$ A) $\frac{\pi}{2}$. B) 1. C) -1. D) $\pi$. Show Answer Correct Answer: B) 1. 55. Using the Fundamental Theorem of Calculus, evaluate $\int_{-1}^{1} x dx$ A) 0. B) -1. C) 1. D) 2. Show Answer Correct Answer: A) 0. 56. $\int_{ }^{ }\left(-24x^5-10x\right)dx$ A) $-4x^6-5x^2+C$. B) $-24x^6-10x^2+C$. C) $-4x^5-5x+C$. D) $-4x^6-10+C$. Show Answer Correct Answer: A) $-4x^6-5x^2+C$. 57. $\int_{ }^{ }x\left(1-3x^2\right)^4dx$ A) $\frac{-1}{30}\left(1-3x^2\right)^5$. B) $\frac{-1}{30}\left(1-3x^2\right)^5+C$. C) $\frac{-1}{6}\left(1-3x^2\right)^5+C$. D) $\left(1-3x^2\right)^5+C$. Show Answer Correct Answer: B) $\frac{-1}{30}\left(1-3x^2\right)^5+C$. 58. Evaluate the definite integral. $\int_0^2\\frac{3x^2-1}{x^2}dx$ A) $\frac{11}{3}$. B) $\frac{13}{2}$. C) $\frac{11}{2}$. D) $\frac{12}{3}$. Show Answer Correct Answer: B) $\frac{13}{2}$. 59. $\int_{ }^{ }\csc\left(x\right)\cot\left(x\right)dx$ A) $\tan\left(x\right)+C$. B) $-\csc\left(x\right)+C$. C) $-\cot^2\left(x\right)+C$. D) $\frac{1}{\tan\left(x\right)}+C$. Show Answer Correct Answer: B) $-\csc\left(x\right)+C$. 60. Which of the following expressions is equivalent to $\sin^2\theta$ A) $\frac{1-\cos2\theta}{2}$. B) $\frac{1-\sin2\theta}{2}$. C) $\frac{1+\cos2\theta}{2}$. D) $\frac{1+\sin2\theta}{2}$. Show Answer Correct Answer: A) $\frac{1-\cos2\theta}{2}$. ← 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 3Class 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