This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 7 Integrals – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 2 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. If $f\left(x\right)=-2x^3-3x^2+5$ $\left[0, 1\right]$ A) $4.06$. B) 4.06 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $4.06$. 2. Find the antiderivative of $f\left(x\right)=4x^2-6x+8$ A) $F\left(x\right)=4x^3-6x^2+8x+C$. B) $F\left(x\right)=2x^3-2x^2+8x+C$. C) $F\left(x\right)=\frac{4}{3}x^3-3x^2+8x+C$. D) $F\left(x\right)=8x-6+C$. Show Answer Correct Answer: C) $F\left(x\right)=\frac{4}{3}x^3-3x^2+8x+C$. 3. $\int_0^1\left(\left(3x\right)^2+1\right)dx=$ A) $\frac{7}{2}$. B) $9$. C) $2$. D) $4$. Show Answer Correct Answer: D) $4$. 4. Find the antiderivative of:$\int_{ }^{ }\left(e^x-\cos\left(x\right)\right)dx$ A) $e^x-\sin\left(x\right)$. B) $e^x+\sin\left(x\right)+c$. C) $e^x-\sin\left(x\right)+c$. D) $e^{2x}-\sin\left(x\right)+c$. Show Answer Correct Answer: C) $e^x-\sin\left(x\right)+c$. 5. What is the area under the curve of $y = \sin(x)$ $x = 0$ $x = \pi$ A) 1. B) $\pi$. C) 2. D) $\frac{\pi}{2}$. Show Answer Correct Answer: C) 2. 6. Evaluate $\int8x^{-3}dx$ A) $-4x^{-2}+c$. B) -4x-2+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $-4x^{-2}+c$. 7. Calculate the integral of 1/x from x = 1 to x = 2. A) Ln(2). B) Ln(1). C) Ln(3). D) 1. Show Answer Correct Answer: A) Ln(2). 8. $\int_0^{\ln2}\left(\frac{e^x}{1+2e^x}\right)dx$ A) 1/2(ln(5)-ln(3)). B) 1/2. C) 0. D) E/2. Show Answer Correct Answer: A) 1/2(ln(5)-ln(3)). 9. What is the answer to page 5, #6? A) D. B) E. C) A. D) B. E) C. Show Answer Correct Answer: D) B. 10. Which of the following is equivalent to:$\int_7^3h\left(\alpha\right)d\alpha+\int_3^9h\left(\alpha\right)d\alpha$ A) $-\int_3^7h\left(\alpha\right)d\alpha$. B) $-\int_7^9h\left(\alpha\right)d\alpha$. C) $\int_7^9h\left(\alpha\right)d\alpha$. D) None of the following are equivalent to the given. Show Answer Correct Answer: C) $\int_7^9h\left(\alpha\right)d\alpha$. 11. Evaluate $\int5x^3+2x\\dx$ A) $\frac{1}{5}x^4+\frac{1}{2}x^2+C$. B) $\frac{5}{4}x^4+x^2+C$. C) $15x^2+2+C$. D) $5x^4+2x^2+C$. Show Answer Correct Answer: B) $\frac{5}{4}x^4+x^2+C$. 12. If $\int_2^{10}f\left(x\right)dx=-6$ $\int_2^{10}-2f\left(x\right)dx$ A) 12. B) 4. C) -12. D) -8. Show Answer Correct Answer: A) 12. 13. $\int_{ }^{ }\frac{x^7}{7}dx$ A) $\frac{x^8}{15}+C$. B) $\frac{x^8}{56}+C$. C) $x^8+C$. D) $\frac{x^8}{8}+C$. Show Answer Correct Answer: B) $\frac{x^8}{56}+C$. 14. $\int_{ }^{ }e^xdx$ A) $xe^x+C$. B) $\frac{1}{e^x}+C$. C) $e^{x^2}+C$. D) $e^x+C$. Show Answer Correct Answer: D) $e^x+C$. 15. $\int\\frac{4x+3}{x^2+3x}dx$ A) $\ln\left|x\right|+3\ln\left|x+3\right|+c$. B) $\ln\left|x\right|+\ln\left|x+3\right|+c$. C) $\ln\left|x^2+3x\right|+c$. D) $3\ln\left|x\right|+\ln\left|x+3\right|+c$. Show Answer Correct Answer: A) $\ln\left|x\right|+3\ln\left|x+3\right|+c$. 16. Which of the following is equivalent to:$\int_2^9g\left(w\right)dw-\int_2^5g\left(w\right)dw$ A) $\int_2^5g\left(w\right)dw$. B) $\int_5^9g\left(w\right)dw$. C) $\int_5^2g\left(w\right)dw$. D) None of the following are equivalent to the given. Show Answer Correct Answer: B) $\int_5^9g\left(w\right)dw$. 17. $\int_1^5\left(-x^2+6x-10\right)dx$ A) 28. B) $\frac{28}{3}$. C) $\frac{-28}{3}$. D) $-\frac{7}{2}$. Show Answer Correct Answer: C) $\frac{-28}{3}$. 18. What is the answer to page 3, #1? A) D. B) E. C) C. D) A. E) B. Show Answer Correct Answer: E) B. 19. What is the antiderivative of $f(x) = 6x$ A) $x^6 + C$. B) $3x^2 + C$. C) $12x + C$. D) $6x^2 + C$. Show Answer Correct Answer: B) $3x^2 + C$. 20. Evaluate $\int\left(\frac{1}{x^2}+\frac{6}{x^3}\right)dx$ A) $-x^{-1}-3x^{-2}+c$. B) -x-1-3x-2+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $-x^{-1}-3x^{-2}+c$. 21. The area of the region bounded by the curve y = x$^{2}$ and the line y = 16 A) 128/3. B) 256/3. C) 64/3. D) 32/3. Show Answer Correct Answer: B) 256/3. 22. $\int_0^2\int_0^{z^2}\int_0^{\left(y-z\right)}\left(2x-y\right)dxdydz$ A) $\frac{16}{15}$. B) $1$. C) $\frac{14}{15}$. D) $\frac{13}{15}$. Show Answer Correct Answer: A) $\frac{16}{15}$. 23. $\int\left(\sqrt{x}^{ }+4e^{4x}+5\right)dx$ A) $x^{\frac{3}{2}}+e^{4x}+5x+c$. B) $\frac{2}{3}x^{\frac{3}{2}}+4e^{4x}+5x+c$. C) $\sqrt{x}+e^{4x}+5x+c$. D) $\frac{2}{3}x^{\frac{3}{2}}+e^{4x}+5x+c$. Show Answer Correct Answer: D) $\frac{2}{3}x^{\frac{3}{2}}+e^{4x}+5x+c$. 24. Use the trapezoidal rule with n = 4 to estimate (to the nearest thousandth) $\int_1^2\left(\frac{1}{1+x^3}\right)dx$ A) .257. B) .514. C) 2.056. D) 1.028. Show Answer Correct Answer: A) .257. 25. Evaluate $\int7x-9x_{ }^{-3}-2\\dx$ A) $F\left(x\right)=\frac{7}{2}x^2+\frac{9}{2}x^{-2}-2x+C$. B) $F\left(x\right)=7x^0-9x^{-4}-2x^{-1}+C$. C) $F\left(x\right)=7x^2-9x^{-2}-2x+C$. D) $F\left(x\right)=7+27x^{-4}+C$. Show Answer Correct Answer: A) $F\left(x\right)=\frac{7}{2}x^2+\frac{9}{2}x^{-2}-2x+C$. 26. $\int_0^{\pi/2}\int_0^1\cos ydxdy$ A) 2. B) 1. C) 0. D) -1. Show Answer Correct Answer: B) 1. 27. What is the meaning of the following symbol:$\int_a^bf\left(x\right)dx$ A) The rate at which f(x) is changing from x = a to x = b. B) The area from the curve to the x-axis from x = a to x = b. C) The area from the curve to the y-axis from x = a to x = b. D) The volume when the curve is rotated about the x-axis from x = a to x = b. Show Answer Correct Answer: B) The area from the curve to the x-axis from x = a to x = b. 28. Find the number(s) c guaranteed by the MVT for integrals. $\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}}\left(\sec x\tan x\right)dx$ A) 0. B) $\frac{-\pi}{4}$. C) There is no c on [0, 4] that satisfies the MVT for integrals. D) $\frac{\pi}{4}$. Show Answer Correct Answer: A) 0. 29. $\int_0^1\int_0^xf\left(x, y\right)dydx=_{ }$ A) $\int_1^0\int_x^0f\left(x, y\right)dydx$. B) $\int_y^1\int_0^1xydxdy$. C) $\int_0^1\int_y^1f\left(x, y\right)dxdy$. D) $\int_0^x\int_0^1f\left(x, y\right)dydx$. Show Answer Correct Answer: C) $\int_0^1\int_y^1f\left(x, y\right)dxdy$. 30. The integration of f(x)= 1/x dx A) -x$^{2}$/2. B) -2x$^{2}$. C) Ln IxI + C. D) X$^{2}$ /2. Show Answer Correct Answer: C) Ln IxI + C. 31. $\int\int\left(3x^2+2y\right)dxdy$ A) $x^2y^3+xy+C$. B) $x^3y^2+xy^2+C$. C) $xy\left(y^2+x\right)+C$. D) $xy\left(x^2+y\right)+C$. Show Answer Correct Answer: D) $xy\left(x^2+y\right)+C$. 32. The equal double integral in polar co-ordinates of $\int_0^{\infty}\int_0^{\infty}e^{-(x^2+y^2)}dxdy$ A) $\int_0^{\infty}\int_0^{\infty}e^{-(r^2+\theta^2)}drd\theta$. B) $\int_0^{\pi/2}\int_0^1e^{-r^2}drd\theta$. C) $\int_0^{\pi/2}\int_0^{\infty}e^{-r^2}rdrd\theta$. D) $\int_0^{\infty}\int_0^{\infty}e^{-r^2}drd\theta$. Show Answer Correct Answer: C) $\int_0^{\pi/2}\int_0^{\infty}e^{-r^2}rdrd\theta$. 33. Evaluate $\int_0^3\frac{dx}{x-2}$ A) Diverges. B) Ln1-ln2. C) Ln(1/2). D) -0.693. Show Answer Correct Answer: A) Diverges. 34. The area under the curve y = sinx over the interval $\left[0, \frac{\pi}{2}\right]$ A) 2 sq.units. B) 4 sq . units. C) 1 sq. units. D) 3 sq. units. Show Answer Correct Answer: C) 1 sq. units. 35. $\int_{ }^{ }\\sec^2\left(x\right)dx$ A) $\sec\left(x\right)\tan\left(x\right)+C$. B) $\frac{1}{3}\sec^3\left(x\right)+C$. C) $\tan^2\left(x\right)+C$. D) $\tan\left(x\right)+C$. Show Answer Correct Answer: D) $\tan\left(x\right)+C$. 36. $2\pi\int_0^1\left(y+1\right)\sqrt{1-y}dy$ A) $\frac{14}{15}$. B) $\frac{-14}{15}$. C) $\frac{-28\pi}{15}$. D) $\frac{28\pi}{15}$. Show Answer Correct Answer: D) $\frac{28\pi}{15}$. 37. $\int\\sin\left(4x-5\right)dx$ A) $-\cos\left(4x-5\right)+c$. B) $4\cos\left(4x-5\right)+c$. C) $-\frac{1}{4}\cos\left(4x-5\right)+c$. D) $\frac{1}{4}\sin\left(4x-5\right)+c$. Show Answer Correct Answer: C) $-\frac{1}{4}\cos\left(4x-5\right)+c$. 38. What is the area under the curve of $y = x^2$ $x = 1$ $x = 3$ A) $\frac{28}{3}$. B) $\frac{26}{3}$. C) 9. D) $\frac{20}{3}$. Show Answer Correct Answer: B) $\frac{26}{3}$. 39. Find the enclosed area by the curve with equation $y=4-x^2$ A) 11. B) 9. C) 7. D) 5. Show Answer Correct Answer: B) 9. 40. Integrate $\int_{ }^{ }x^{\frac{1}{3}}dx$ A) $=\frac{3}{4}x^{\frac{4}{3}}+c$. B) $=\frac{1}{3}x^{-\frac{2}{3}}+c$. C) $=\frac{4}{3}x^{\frac{4}{3}}+c$. D) $=\frac{3}{2}x^{\frac{2}{3}}+c$. Show Answer Correct Answer: A) $=\frac{3}{4}x^{\frac{4}{3}}+c$. 41. Both double and triple integrals give the volume under a surface. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 42. $\int_{ }^{ }\left(2x-1\right)^2dx$ A) $\frac{4}{3}x^3-x^2+x+c$. B) $\left(x^2-x\right)^2+c$. C) $\frac{\left(2x-1\right)^3}{3}+c$. D) $\frac{4x^3}{3}-2x^2+x+c$. Show Answer Correct Answer: D) $\frac{4x^3}{3}-2x^2+x+c$. 43. The integral represents ..... A) A variable. B) The area under a curve. C) A derivative. D) When you have integrity. Show Answer Correct Answer: B) The area under a curve. 44. Using the Fundamental Theorem of Calculus, evaluate $\int_{0}^{2} 3x^2 dx$ A) 16. B) 8. C) 12. D) 4. Show Answer Correct Answer: C) 12. 45. There are a finite number of antiderivatives for any f'(x). A) True. B) False, infinite. C) All the above. D) None of the above. Show Answer Correct Answer: B) False, infinite. 46. $\int_{ }^{ }\frac{e^3}{5}dx$ A) $\frac{3e^3}{5}+C$. B) $\frac{e^4}{20}+C$. C) $\frac{e^4}{9}+C$. D) $\frac{xe^3}{5}+C$. Show Answer Correct Answer: D) $\frac{xe^3}{5}+C$. 47. What is the solution of $\int_0^3\left(3x^2\right)dx$ A) 27. B) 23. C) 21. D) 25. Show Answer Correct Answer: A) 27. 48. There are ..... cases of L'Hopital's rule. A) 2. B) 7. C) 5. D) 8. Show Answer Correct Answer: B) 7. 49. What is the answer to page 5, #7? A) B. B) C. C) E. D) A. E) D. Show Answer Correct Answer: C) E. 50. $\int_{ }^{ }\frac{\pi}{x}dx$ A) $\frac{\pi x}{0}+C$. B) $\pi\ln\left(x\right)+C$. C) $\frac{\ln\left(\pi\right)}{x}+C$. D) $\ln\left(\frac{\pi}{x}\right)+C$. Show Answer Correct Answer: B) $\pi\ln\left(x\right)+C$. 51. $\frac{d}{dx}\left(\sin^{-1}x\right)$ A) $-\frac{1}{\sqrt{1-x^2}}$. B) $\cos^{-1}x$. C) $\frac{1}{\sqrt{1-x^2}}$. D) $-\cos^{-1}x$. Show Answer Correct Answer: C) $\frac{1}{\sqrt{1-x^2}}$. 52. What is the area of the region enclosed by the graphs of f(x)=x-2x$^{2}$ and g(x)=-5x? A) 16/3. B) 20/3. C) 7/3. D) 9. Show Answer Correct Answer: D) 9. 53. $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\left(1+\sin3t\right)\left(\cos3t\right)dt=$ A) 0. B) 1. C) 1/2. D) -1/2. Show Answer Correct Answer: D) -1/2. 54. $\int_0^2\int_0^yx^2dxdy$ A) $\frac{2}{3}$. B) $\frac{1}{3}$. C) $\frac{5}{3}$. D) $\frac{4}{3}$. Show Answer Correct Answer: D) $\frac{4}{3}$. 55. Calculate the definite integral of 3x from 1 to 4. A) 15. B) 22.5. C) 30. D) 10. Show Answer Correct Answer: B) 22.5. 56. Evaluate:$\int_2^{\infty}\frac{1}{x^2}dx$ A) Diverges. B) $3$. C) $1$. D) $\frac{1}{2}$. E) $\ln2$. Show Answer Correct Answer: D) $\frac{1}{2}$. 57. A midpoint approximation will be the average of the left and right hand Riemann Sums. A) Always. B) Sometimes. C) Never. D) None of the above. Show Answer Correct Answer: B) Sometimes. 58. $\int_{ }^{ }x^3dx$ A) $\frac{1}{3}x^3+c$. B) $x^4+c$. C) $3x^2+c$. D) $\frac{1}{4}x^4+c$. Show Answer Correct Answer: D) $\frac{1}{4}x^4+c$. 59. $\int_0^{\pi}24\sin\left(6x\right)\cos\left(6x\right)dx=$ A) 0. B) 4/3. C) -4/3. D) -8/3. Show Answer Correct Answer: A) 0. 60. $\int_{ }^{ }\left[5^x-\csc^2x\right]dx$ A) $\frac{5^x}{\ln5}+\cot x+C$. B) $5^x-\cot x+C$. C) $\frac{5^x}{\ln x}-\cot x+C$. D) $5^x+\cot x+C$. Show Answer Correct Answer: A) $\frac{5^x}{\ln5}+\cot x+C$. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 7 Integrals Quiz 1Class 12 Mathematics Chapter 7 Integrals Quiz 3Class 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