This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 7 Integrals – Quiz 5 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 5 (53 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find the antiderivative of $f(x) = \frac{1}{x}$ A) $\ln|x| + C$. B) $\ln|x^2| + C$. C) $\frac{1}{2}x^2 + C$. D) $x\ln|x| + C$. Show Answer Correct Answer: A) $\ln|x| + C$. 2. $\int_2^1\int_0^1\left(x+y\right)^2dxdy$ A) $\frac{39}{6}$. B) $-\frac{17}{3}$. C) -6. D) $-\frac{25}{6}$. Show Answer Correct Answer: D) $-\frac{25}{6}$. 3. Evaluate the Integral $\int2x\cos\left(x^2\right)dx$ A) $\frac{1}{2}\sin\left(x^2\right)+C$. B) $4\cos\left(2x\right)+C$. C) $\sin\left(x^2\right)+C$. D) $2\sin\left(2x\right)+C$. Show Answer Correct Answer: C) $\sin\left(x^2\right)+C$. 4. $\int_0^2\int_0^2xdxdy$ A) 2. B) 4. C) 3. D) 1. Show Answer Correct Answer: B) 4. 5. Approximate the area under the curve $f\left(x\right)=-\frac{5}{x}$ A) $\frac{3545}{693}$. B) $\frac{3083}{693}$. C) $\frac{7552}{693}$. D) $\frac{3776}{693}$. Show Answer Correct Answer: D) $\frac{3776}{693}$. 6. For a function that is strictly increasing, a right hand Riemann Sum is which of the following: A) Overestimate. B) Unable to Determine. C) Underestimate. D) Exact Solution. Show Answer Correct Answer: A) Overestimate. 7. Ten years ago, a school with a fixed population decided to increase the size of its student body. The size of the student body t years since the increase began is given as s(t). It is known that the value of the definite integral from 0 to 10 of s'(t) is 400. Which is true? A) Nothing can be determined from this information. B) The student body is increasing by 400 per year. C) The student body grew by 400 students. D) The student body is now at 400. Show Answer Correct Answer: C) The student body grew by 400 students. 8. True or false:since every function has a derivative, every function has an antiderivative. A) True. B) False. C) Eh well, uh I mean . D) None of the above. Show Answer Correct Answer: C) Eh well, uh I mean . 9. Given that the demand function D(x) and the supply function S(x) of a product are given as $D(x)=12-x$ $S\left(x\right)=x+6$ A) RM4.50. B) RM2.50. C) RM3. D) RM9. Show Answer Correct Answer: A) RM4.50. 10. Evaluate:$\int e^{2x}dx$ A) $e^{2x}+C$. B) $e^{3x}+C$. C) $2e^{2x}+C$. D) $\frac{1}{2}e^{2x}+C$. Show Answer Correct Answer: D) $\frac{1}{2}e^{2x}+C$. 11. Evaluate the indefinite integral. $\int\left(4\csc x\cot x-6\cos x\right)dx$ A) $-4\csc x+6\sin x+C$. B) $4\cot x-6\sin x+C$. C) $-4\csc x-6\sin x+C$. D) $4\csc x+6\sin x+C$. Show Answer Correct Answer: C) $-4\csc x-6\sin x+C$. 12. Integrate the following indefinite integral via u-substitution $\int_{ }^{ }\left(2+2x\right)e^{\left(4x+2x^2\right)}dx$ A) $e^{\frac{1}{2}\left(4x+2x^2\right)}+C$. B) $\frac{1}{2}e^{\left(4x+2x^2\right)}+C$. C) $2e^{\left(4x+2x^2\right)}+C$. D) $e^{2\left(4x+2x^2\right)}+C$. Show Answer Correct Answer: B) $\frac{1}{2}e^{\left(4x+2x^2\right)}+C$. 13. What is the relationship between the derivative and the integral? A) The derivative is a type of integral. B) The integral measures the rate of change. C) The derivative and the integral are inverse operations. D) The derivative and the integral are unrelated concepts. Show Answer Correct Answer: C) The derivative and the integral are inverse operations. 14. $\int\sqrt{x^5}dx= ..... $ A) $\frac{2}{7}\sqrt{x^7}+c$. B) $\frac{7}{2}\sqrt{x^7}+c$. C) $\frac{7}{2\sqrt{x^7}}+c$. D) $\frac{2}{7\sqrt{x^7}}+c$. Show Answer Correct Answer: A) $\frac{2}{7}\sqrt{x^7}+c$. 15. $\int_{ }^{ }8\left(1+2x\right)^{-3}dx=\frac{-2}{\left(1+2x\right)^2}+c$ A) CORRECT/ BETUL. B) WRONG/ SALAH. C) All the above. D) None of the above. Show Answer Correct Answer: A) CORRECT/ BETUL. 16. Trapezozidal rule is NOT the method of finding the exact value of a definite integral.This statement is A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 17. $\frac{\cos x}{\left(1+\sin x\right)\left(2+\sin x\right)}$ A) $\log\left(1+\sin x\right)\left(2+\sin x\right)$. B) $\log\frac{2+\sin x}{1+\sin x}$. C) $\log\frac{\left(1+\sin x\right)}{2+\sin x}$. D) None of the above. Show Answer Correct Answer: C) $\log\frac{\left(1+\sin x\right)}{2+\sin x}$. 18. Triple integrals give: A) Heart attack. B) Mass & volume. C) Headache. D) Mass only. Show Answer Correct Answer: B) Mass & volume. 19. If $\int_2^{10}f\left(x\right)dx=-6$ $\int_2^{10}\\frac{1}{3}f\left(x\right)dx$ A) -18. B) 18. C) 2. D) -2. Show Answer Correct Answer: D) -2. 20. Given v(t) = x$^{-9}$, find the general equation for the antiderivative. A) (-1/8)x$^{-8 }$+ C. B) (1/8)x$^{-8}$ + C. C) (1/10)x$^{10}$. D) (-1/8)x$^{-8}$. Show Answer Correct Answer: A) (-1/8)x$^{-8 }$+ C. 21. $\int_1^35x^2dx$ A) 19/3. B) 130/3. C) 43. D) 40. Show Answer Correct Answer: B) 130/3. 22. Evaluate $\int\left(x^{-1}-1\right)dx$ A) $\ln x-x+c$. B) Lnx-x+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\ln x-x+c$. 23. $\int\frac{1}{x}dx$ A) Ln|x| + C. B) $\frac{1}{x^2}$. C) 1 + C. D) $-\frac{1}{x^2}$. Show Answer Correct Answer: A) Ln|x| + C. 24. What is the area between the curve $y=-3x^2+12$ $x=0$ $x=2$ A) 24. B) 32. C) 16. D) 12. Show Answer Correct Answer: C) 16. 25. Determine the rule we follow to find the antiderivative of $x^n.$ A) $\frac{x^{\left(n+1\right)}}{n+1}+C$. B) $\left(n+1\right)n^{\left(n+1\right)}+C$. C) $nx^{\left(n-1\right)}+C$. D) $\frac{1}{n-1}x^{\left(n-1\right)}+C$. Show Answer Correct Answer: A) $\frac{x^{\left(n+1\right)}}{n+1}+C$. 26. Find $\int(12x^3-4x)dx$ A) $3x^4-2x^2+c$. B) $12x^4-x^2+c$. C) $3x^4-4x^2+c$. D) $4x^3-2x+c$. Show Answer Correct Answer: A) $3x^4-2x^2+c$. 27. The area under a curve is also known as the ..... ? A) Algebraic area. B) Physical area. C) Antiderivative. D) Integral. Show Answer Correct Answer: B) Physical area. 28. Evaluate the definite integral $\int_0^4 2x \, dx$ A) 4. B) 8. C) 32. D) 16. Show Answer Correct Answer: D) 16. 29. $\int_1^8\left(x^{\frac{1}{3}}+1\right)dx$ A) 13/4. B) 73/4. C) 1. D) -87/4. Show Answer Correct Answer: B) 73/4. 30. According to the Fundamental Theorem of Calculus, if $F$ $f$ $[a, b]$ $\int_a^b f(x) \, dx$ A) $F(b)-F(a)$. B) $F(b) + F(a)$. C) $F(a) + F(b)$. D) $F(a)-F(b)$. Show Answer Correct Answer: A) $F(b)-F(a)$. 31. If $\int_2^{10}f\left(x\right)dx=-6$ $\int_{10}^2f\left(x\right)dx$ A) 10. B) 2. C) 6. D) -6. Show Answer Correct Answer: C) 6. 32. Find the average value of the function $f\left(x\right)=x+3$ $\left[3, 9\right]$ A) $9$. B) $7.5$. C) $54$. D) $67.5$. Show Answer Correct Answer: A) $9$. 33. $\int\sin\left(x\right)dx$ A) $\sin\left(x\right)$. B) $\cos\left(x\right)$. C) $-\sin\left(x\right)$. D) $-\cos\left(x\right)$. Show Answer Correct Answer: D) $-\cos\left(x\right)$. 34. Given g(x) = x + 2 and G(0) = 3, find G(x). A) X$^{2}$ + 3. B) 1/2 x$^{2}$ + 2x + 6. C) 1/2 x$^{2}$ + 2x + 3. D) X$^{2}$ + 2x + 6. Show Answer Correct Answer: C) 1/2 x$^{2}$ + 2x + 3. 35. What is the average value of $f\left(x\right)=\sqrt{4-x^2}$ $\left[0, 2\right]$ A) $2\pi$. B) $\frac{\pi}{2}$. C) $\pi$. D) $\frac{\pi}{4}$. Show Answer Correct Answer: B) $\frac{\pi}{2}$. 36. Which of the following is equivalent to:$\int_2^9f\left(\theta\right)d\theta-\int_4^9f\left(\theta\right)d\theta$ A) $\int_2^4f\left(\theta\right)d\theta$. B) $\int_4^2f\left(\theta\right)d\theta$. C) $\int_2^7f\left(\theta\right)d\theta$. D) None of the following are equivalent to the given. Show Answer Correct Answer: A) $\int_2^4f\left(\theta\right)d\theta$. 37. Evaluate the following definite integral via u-substitution $\int_0^118x^2\left(2x^3+1\right)^2dx$ A) $\frac{1}{3}$. B) $\frac{26}{3}$. C) $1$. D) $26$. Show Answer Correct Answer: D) $26$. 38. Integration is the inverse of differentiation but it applications it can be used to ..... A) Find the area under a curve. B) Calculate the force of an object. C) Find the altitude of an objects perimeter. D) None of the above. Show Answer Correct Answer: A) Find the area under a curve. 39. Find the area under a curve defined by the equation 5x$^{4}$+3x+7 between the x values 0 and 4. A) 1200. B) 1134. C) 1076. D) 1/12. Show Answer Correct Answer: C) 1076. 40. What is the area under the curve of $y = 4-x^2$ $x =-2$ $x = 2$ A) 16. B) 32/3. C) 16/3. D) 8. Show Answer Correct Answer: B) 32/3. 41. $\int_1^2\int_3^4\left(2x-7y\right)dxdy$ A) -1.50. B) -3.50. C) 1.50. D) 3.50. Show Answer Correct Answer: B) -3.50. 42. Evaluate $\int e^xdx$ A) $e^{\frac{1}{2}x^2}+C$. B) $e^{2x^2}+C$. C) $2e^{2x}+C$. D) $e^x+C$. Show Answer Correct Answer: D) $e^x+C$. 43. Calculate the average value of the function $f(x) = 2x + 3$ $[1, 4]$ A) 5. B) 11. C) $\frac{11}{2}$. D) $\frac{5}{2}$. Show Answer Correct Answer: C) $\frac{11}{2}$. 44. $\int\\frac{6x+5}{\sqrt[]{x}}dx$ A) $\frac{3}{\sqrt[]{x}}-\frac{5}{2\\sqrt[]{x^3}}+c$. B) $4\\sqrt[]{x^3}+10\\sqrt[]{x}+c$. C) $\frac{9}{\sqrt[]{x^3}}+c$. D) $9\\sqrt[]{x^3}+\frac{5}{2}\\sqrt[]{x}+c$. Show Answer Correct Answer: B) $4\\sqrt[]{x^3}+10\\sqrt[]{x}+c$. 45. Find the antiderivative:$\int_{ }^{ }5x^6dx$ A) $x^6+C$. B) $\frac{5x^7}{7}+C$. C) $x^6$. D) $\frac{5x^7}{7}$. Show Answer Correct Answer: B) $\frac{5x^7}{7}+C$. 46. Find the area under the curve y =3x$^{2}$-2x from x= 1 to x =5. A) 99. B) 100. C) 150. D) 152. Show Answer Correct Answer: B) 100. 47. $\int\left(\pi+3\sqrt{x}^{ }\right)dx$ A) $\pi x+\frac{3}{2}\sqrt{x}+c$. B) $\pi x+2\sqrt{x^3}+c$. C) $\frac{\pi^2}{2}+2\sqrt{x^3}+c$. D) $\pi+\frac{2}{3}\sqrt{x}+c$. Show Answer Correct Answer: B) $\pi x+2\sqrt{x^3}+c$. 48. $\int_1^2\left(2x+k\right)dx=8.$ $\k=?$ A) $-2$. B) $4$. C) $-3$. D) $5$. Show Answer Correct Answer: D) $5$. 49. $\int\left(\frac{1}{x^3}\right)dx$ A) $-\frac{1}{2x^2}+C$. B) $\frac{1}{x^2}$. C) $-\frac{3}{x^4}$. D) Ln| $x^3$. Show Answer Correct Answer: A) $-\frac{1}{2x^2}+C$. 50. Set up limit of triple integral to find the volume of the solid that lies below the hemisphere $z=\sqrt{25-x^2-y^2}$ $x^2+y^2=16$ $x^2+y^2=25$ A) $\int_0^{2\pi}\int_4^5\int_0^{\sqrt{25-r^2}}rdzdrd\theta$. B) $\int_0^{2\pi}\int_4^5\int_0^5rdzdrd\theta$. C) $\int_0^{2\pi}\int_0^5\int_0^{\sqrt{25-r^2}}rdzdrd\theta$. D) $\int_0^{2\pi}\int_0^4\int_0^{\sqrt{25-r^2}}rdzdrd\theta$. Show Answer Correct Answer: A) $\int_0^{2\pi}\int_4^5\int_0^{\sqrt{25-r^2}}rdzdrd\theta$. 51. $\int\frac{1}{\sqrt{1-x^2}}dx$ A) $\arcsin\left(x\right)+C$. B) $-4x\sqrt{1-x^2}+C$. C) $2\sqrt{1-x^2}+C$. D) $\arccos\left(x\right)+C$. Show Answer Correct Answer: A) $\arcsin\left(x\right)+C$. 52. Integrate $\frac{1}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ A) $-\left(1+\frac{1}{x^4}\right)^{\frac{1}{4}}$. B) $\left(x^4+1\right)^{\frac{1}{4}}$. C) $-\left(1+\frac{1}{x^4}\right)^{\frac{3}{4}}$. D) None of the above. Show Answer Correct Answer: A) $-\left(1+\frac{1}{x^4}\right)^{\frac{1}{4}}$. 53. $\int_{ }^{ }\\frac{4}{\sqrt{x}}dx$ A) $8\sqrt{x}+C$. B) $2\sqrt{x}+C$. C) $\frac{4x}{\sqrt{x}}+C$. D) None of these. Show Answer Correct Answer: A) $8\sqrt{x}+C$. ← PreviousRelated 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 4Class 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