This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 7 Integrals – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 1 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Evaluate $\int\left(5x^2-7x+6\right)dx$ A) $\frac{5}{3}x^3-\frac{7}{2}x^2+6x+c$. B) 35x3-27x2+6x+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\frac{5}{3}x^3-\frac{7}{2}x^2+6x+c$. 2. $\frac{d}{dx}\left(\sin x\right)$ A) $\cos x$. B) $-\cos x$. C) $\sin x\cos x$. D) None of these. Show Answer Correct Answer: A) $\cos x$. 3. Which definite integral corresponds to the infinite Riemann Sum $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left(2x_i-\sin x_i\right)\Delta x$ $\left[0, \frac{\pi}{4}\right]$ A) $\int_0^{\frac{\pi}{4}}\left(2x-\sin x\right)dx$. B) $\int_1^{\infty}\left(2x-\sin\left(\frac{\pi}{4}\right)\right)dx$. C) $\int_1^{\infty}\left(2x-\sin x\right)dx$. D) $\int_{\frac{\pi}{4}}^{\infty}\left(2x-\sin x\right)dx$. Show Answer Correct Answer: A) $\int_0^{\frac{\pi}{4}}\left(2x-\sin x\right)dx$. 4. Which property of a graph will cause a left Riemann sum to be an overestimate? A) Decreasing. B) Concave down. C) Concave up. D) Increasing. Show Answer Correct Answer: A) Decreasing. 5. $\int_{ }^{ }f'\left(x\right)dx$ A) $f\left(\frac{x^2}{2}\right)+C$. B) $f\left(x\right)+C$. C) $f" \left(x\right)+C$. D) $\frac{f^2\left(x\right)}{2}+C$. Show Answer Correct Answer: B) $f\left(x\right)+C$. 6. $\int_{-1}^03e^xdx=$ A) $3+3e$. B) $e^3-e$. C) $-\frac{3}{e}$. D) $3-\frac{3}{e}$. Show Answer Correct Answer: D) $3-\frac{3}{e}$. 7. $\int_e^{e^3}\frac{2}{x}dx=$ A) $e^6-2$. B) 4. C) 5. D) 6. Show Answer Correct Answer: B) 4. 8. Another word for 'integral' is ..... A) Antiderivative. B) Derivative. C) Theorem. D) Constant. Show Answer Correct Answer: A) Antiderivative. 9. If $a\in R$ $\int_1^a\left(4x-1\right)dx=5$ $a= ..... $ A) 3. B) $\frac{3}{2}$. C) -2. D) $\frac{2}{3}$. E) 2. Show Answer Correct Answer: E) 2. 10. Which of the following is equivalent to:$\int_0^3f\left(x\right)dx+\int_3^7f\left(x\right)dx$ A) 7. B) $\int_0^7f\left(x\right)dx$. C) $\int_7^0f\left(x\right)dx$. D) None of the following are equivalent to the given. Show Answer Correct Answer: B) $\int_0^7f\left(x\right)dx$. 11. A particle moves along the x-axis with velocity given by v(t) = 3t$^{2}$-4 for time t $\geq$ 0. If the particle is at position x =-2 at time t = 0, what is the position of the particle at time t = 3? A) 16. B) 13. C) 15. D) 25. E) 17. Show Answer Correct Answer: B) 13. 12. $\int\\frac{2x^2+x+4}{\left(x+2\right)\left(1+x^2\right)}dx$ A) $\ln\left|x^3+2x^2+x+2\right|+c$. B) $2\ln\left|x+2\right|+\ln\left|1+x^2\right|+c$. C) $2\ln\left|x+2\right|+\sin^{-1}x+c$. D) $2\ln\left|x+2\right|+\tan^{-1}x+c$. Show Answer Correct Answer: D) $2\ln\left|x+2\right|+\tan^{-1}x+c$. 13. $\int_0^3\int_0^3\int_0^3dxdydz$ A) 27. B) 9. C) 6. D) 3. Show Answer Correct Answer: A) 27. 14. $\int_{ }^{ }0dx$ A) $0$. B) $C$. C) $dx+C$. D) $x+C$. Show Answer Correct Answer: B) $C$. 15. Find the antiderivative off'(x) = x$^{2}$ when f(3) = 11. A) X$^{3}$ + 11. B) X$^{3}$ + 29. C) (1/3)x$^{3}$ + 9. D) (1/3)x$^{3}$+ 2. Show Answer Correct Answer: D) (1/3)x$^{3}$+ 2. 16. $\int_0^0\left(\sin x\right)dx$ A) 2. B) 1. C) 4. D) 0. Show Answer Correct Answer: D) 0. 17. Approximate the area using a Midpoint Riemann Sum on the interval [0, 4] for $f\left(x\right)=x^2+3$ A) 42. B) 66. C) 33. D) 26. Show Answer Correct Answer: C) 33. 18. $\int_{\frac{\pi}{4}}^{\pi}2\sin xdx$ A) $-2+2\sqrt{2}$. B) $2+\sqrt{2}$. C) $-2-\sqrt{2}$. D) $2+\sqrt{3}$. Show Answer Correct Answer: B) $2+\sqrt{2}$. 19. $\int_{-1}^1\left(2x-1\right)\left(2x+1\right)dx=$ A) $-1.5$. B) $\frac{2}{3}$. C) 3. D) $-\frac{2}{3}$. Show Answer Correct Answer: B) $\frac{2}{3}$. 20. Evaluate:$\int\left(\frac{2x^3+1}{x^2}\right)dx$ A) $x^2-\frac{1}{x}+C$. B) $x^3-x^2+C$. C) $\frac{1}{2}x^2-\frac{1}{x}+C$. D) $\frac{2}{3}x^3+\frac{1}{x}+C$. Show Answer Correct Answer: A) $x^2-\frac{1}{x}+C$. 21. Using the Fundamental Theorem of Calculus, evaluate $\int_{0}^{3} (2x + 1) dx$ A) 12. B) 9. C) 15. D) 18. Show Answer Correct Answer: A) 12. 22. $\frac{d}{dx}\left(\sinh x\right)$ A) $\cosh x$. B) $-\cosh x$. C) $-\operatorname{csch}x$. D) None of these. Show Answer Correct Answer: A) $\cosh x$. 23. Write the given expression using summation notation. $2\left(1.5\right)^2+2\left(2\right)^2+2\left(2.5\right)^2+ ..... +2\left(5.5\right)^2$ A) $\sum_{n=1}^9\left(2\left(1+0.5n\right)^2\right)$. B) $\sum_{n=1}^9\left(2\left(0.5n\right)^2\right)$. C) $\sum_{n=0}^8\left(2\left(1+0.5n\right)^2\right)$. D) $\sum_{n=0}^8\left(1+0.56n\right)^2$. Show Answer Correct Answer: A) $\sum_{n=1}^9\left(2\left(1+0.5n\right)^2\right)$. 24. The area of the region bounded by the curve x = 2y + 3 and the lines. y = 1 and y =-1 is (A) 4 sq units (B) 3/2 sq units (C) 6 sq units (D) 8 sq units A) 4 sq.units. B) 3/2 sq.units. C) 6 sq.units. D) 8 sq.units. Show Answer Correct Answer: C) 6 sq.units. 25. $\int_{ }^{ }\left(3-2x\right)^4dx$ A) $-10\left(3-2x\right)^5+c$. B) $-\frac{1}{10}\left(3-2x\right)^5+c$. C) $\frac{\left(3-2x\right)^5}{10}+c$. D) $\frac{\left(3-2x\right)^5}{5}+c$. Show Answer Correct Answer: B) $-\frac{1}{10}\left(3-2x\right)^5+c$. 26. What is the antiderivative of $f(x) = 7$ A) $49x + C$. B) $\frac{1}{7}x + C$. C) $7x^2 + C$. D) $7x + C$. Show Answer Correct Answer: D) $7x + C$. 27. $\int_{ }^{ }\left(\cos\left(x\right)+\sin\left(x\right)\right)dx$ A) $\sin\left(x\right)\cos\left(x\right)+C$. B) $\sin\left(x\right)+\cos\left(x\right)+C$. C) $-\sin\left(x\right)-\cos\left(x\right)+C$. D) $\sin\left(x\right)-\cos\left(x\right)+C$. Show Answer Correct Answer: D) $\sin\left(x\right)-\cos\left(x\right)+C$. 28. $\int_{ }^{ }\cos\left(\pi x\right)dx$ A) $\pi\sin\left(\pi x\right)+C$. B) $-\frac{1}{\pi}\sin\left(\pi x\right)+C$. C) $-\pi\sin\left(\pi x\right)+C$. D) $\frac{1}{\pi}\sin\left(\pi x\right)+C$. Show Answer Correct Answer: D) $\frac{1}{\pi}\sin\left(\pi x\right)+C$. 29. H'(x) = x(3x$^{2}$ + 2)$^{10}$. h(x) = A) (1/11)(3x$^{2}$ + 2)$^{11}$ + C. B) (6/11)(3x$^{2}$ + 2)$^{11}$ + C. C) (1/66)(3x$^{2}$ + 2)$^{11}$ + C. D) (1/6)(3x$^{2}$ + 2)$^{11}$ + C. Show Answer Correct Answer: C) (1/66)(3x$^{2}$ + 2)$^{11}$ + C. 30. What is the answer to page 4, #3? A) C. B) E. C) A. D) B. E) D. Show Answer Correct Answer: A) C. 31. Given that $\int_0^5f\left(x\right)dx=7$ $\int_2^5f\left(x\right)dx=-1$ $\int_0^2f\left(x\right)dx=$ A) $8$. B) 8 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $8$. 32. $\int_4^9\left(3\sqrt{x}\right)dx=$ A) $9\cdot\frac{2}{3}-4\cdot\frac{2}{3}$. B) $\frac{3}{\sqrt{9}}-\frac{3}{\sqrt{4}}$. C) $2\left(27\right)-2\left(8\right)$. D) $3\left(\sqrt{4}\right)^3-3\left(\sqrt{9}\right)^3$. Show Answer Correct Answer: C) $2\left(27\right)-2\left(8\right)$. 33. $\int\frac{\left(x^3+2x^2-4\right)}{x^2}dx$ A) $\frac{1}{2}x^2+2x+\frac{4}{x}+c$. B) $\frac{1}{2}x^2+2+\frac{4}{x}+c$. C) $x+2-\frac{4}{x^2}+c$. D) $x+2x-4x^{-2}+c$. Show Answer Correct Answer: A) $\frac{1}{2}x^2+2x+\frac{4}{x}+c$. 34. $f\left(x\right)=\frac{1}{\sqrt{x}}$ A) 1/5. B) 2/5. C) 2. D) 1. Show Answer Correct Answer: B) 2/5. 35. Evaluate the integral:$\int_{ }^{ }\left(\frac{1}{x^4}\right)dx$ A) $-\frac{1}{3x^3}+c$. B) -3x31+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $-\frac{1}{3x^3}+c$. 36. If you have to find the area under a curve, what would you use? A) A pencil. B) A= bxh. C) Derivation. D) Integration. Show Answer Correct Answer: D) Integration. 37. Evaluate the integral:$\int_{ }^{ }\left(\frac{x^3+x}{x}\right)dx$ A) $\frac{x^3}{3}+x+c$. B) 3x3+x+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\frac{x^3}{3}+x+c$. 38. $\int_{-4}^4\sqrt{16-x^2}dx=$ A) $8\pi$. B) $16\pi$. C) $4\pi$. D) $0$. Show Answer Correct Answer: A) $8\pi$. 39. Choose the correct next step $\int\left(x^2-3\right)^2dx$ A) $\frac{1}{3}\left(x^2-3\right)^3+c$. B) $\int_{ }^{ }\left(x^4+9\right)dx$. C) $\left(\frac{1}{3}x^3-3x\right)^2+c$. D) $\int_{ }^{ }\left(x^4-6x^2+9\right)dx$. Show Answer Correct Answer: D) $\int_{ }^{ }\left(x^4-6x^2+9\right)dx$. 40. Find $\int(2x+3)dx$ A) $x^2+3x$. B) $2x^2+3x+c$. C) $2x^2+3$. D) $x^2+3x+c$. Show Answer Correct Answer: D) $x^2+3x+c$. 41. Find the area under $y=\left(x-2\right)^5$ $\left[2, 4\right]$ A) 16/3. B) 32/3. C) 4. D) 16. Show Answer Correct Answer: B) 32/3. 42. $\int_0^3\left(3x^2-4x\right)dx=$ A) 15. B) 9. C) 16. D) 14. Show Answer Correct Answer: B) 9. 43. $\int\left(5\sqrt{x^3}-16e^{-4x}+\frac{1}{x}\right)dx$ A) $\frac{5}{2}x^{\frac{3}{2}}-16e^{-4x}+\ln\left|x\right|+C$. B) $2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C$. C) Got lazy with fake answers. D) $5x^{\frac{1}{3}}-4e^{-4x}+1+C$. Show Answer Correct Answer: B) $2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C$. 44. Find $y=f\left(x\right)$ $f" \left(x\right)=x^2$ $f'\left(0\right)=7$ $f\left(0\right)=2$ A) $\frac{1}{12}x^4+7x+2$. B) 121x4+7x+2 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\frac{1}{12}x^4+7x+2$. 45. If $\int_{-5}^3g\left(x\right)dx=-2$ $\int_{-5}^{15}g\left(x\right)dx=9$ $\int_{15}^3g\left(x\right)dx$ A) -7. B) 11. C) 7. D) -11. Show Answer Correct Answer: D) -11. 46. Find the value of the indefinite integral. $\int\\frac{4x}{2x^2+6}dx$ A) $4x\ln\left(2x^2+6\right)+C$. B) $\ln\left(2x^2+6\right)+C$. C) $\frac{1}{2x^2+6}+C$. D) $\frac{1}{\left(2x^2+6\right)^2}+C$. Show Answer Correct Answer: B) $\ln\left(2x^2+6\right)+C$. 47. Let $f\left(x\right)=\frac{6}{x^2}$ A) $F\left(x\right)=\frac{18}{x^3}+C$. B) $F\left(x\right)=-\frac{12}{x}+C$. C) $F\left(x\right)=-\frac{6}{x}+C$. D) $F\left(x\right)=-\frac{2}{x^3}+C$. Show Answer Correct Answer: C) $F\left(x\right)=-\frac{6}{x}+C$. 48. $\int_0^2\left(3x-1\right)^3dx=$ A) $25$. B) $\frac{5}{2}$. C) $-5\frac{2}{5}$. D) 52. Show Answer Correct Answer: D) 52. 49. Given the marginal cost function, $C'\left(x\right)=6x^2-3x+5$ A) $C\left(x\right)=2x^3-\frac{3}{2}x^2+$ $5x+8$. B) $C\left(x\right)=12x-3$. C) $C\left(x\right)=2x^3-\frac{3}{2}x^2+$ $5x+k$. D) $C\left(x\right)=2x^3-\frac{3}{2}x^2+$ $5x$. Show Answer Correct Answer: A) $C\left(x\right)=2x^3-\frac{3}{2}x^2+$ $5x+8$. 50. Evaluate $\int\left(x^2-2x\right)dx$ A) $\frac{x^3}{3}-x^2+c$. B) 3x3-x2+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\frac{x^3}{3}-x^2+c$. 51. $\int_1^2f\left(x\right)dx=3$ $\int_1^24f\left(x\right)dx=$ A) $\frac{4}{3}$. B) $12$. C) $7$. D) $-12$. Show Answer Correct Answer: B) $12$. 52. Evaluate the definite integral. $\int_{-1}^23\cdot\text{d}x$ A) 9. B) 3. C) 12. D) 6. Show Answer Correct Answer: A) 9. 53. $\int_2^4\left(x\right)dx$ A) 12. B) 1. C) 6. D) 14. Show Answer Correct Answer: C) 6. 54. For a function that is strictly increasing, a right hand Riemann Sum (Right Endpoint Approximation) is which of the following: A) Underestimate. B) Unable to Determine. C) Overestimate. D) Exact Solution. Show Answer Correct Answer: C) Overestimate. 55. $\int\int\int e^{4x}dxdydz$ A) $\frac{1}{4}e^{4x}yz+C$. B) $\frac{1}{3}e^{4xy}yz+C$. C) $\frac{1}{3}e^{4x}yz+C$. D) $\frac{1}{4}e^{4x}xyz+C$. Show Answer Correct Answer: A) $\frac{1}{4}e^{4x}yz+C$. 56. $\int t^2\left(3t+5\right)dt= ..... $ A) $\frac{3}{4}t^3+\frac{5}{3}t^2+c$. B) $9t^2+10t+c$. C) $3t^4+\frac{3}{5}t^3+c$. D) $\frac{3}{4}t^4+\frac{5}{3}t^3+c$. Show Answer Correct Answer: D) $\frac{3}{4}t^4+\frac{5}{3}t^3+c$. 57. Which of the following equations represents a cone? A) $z=x^2+y^2$. B) $x^2+y^2+z^2=1$. C) $z=\sqrt{x^2+y^2}$. D) $z=x^3+y^3$. Show Answer Correct Answer: C) $z=\sqrt{x^2+y^2}$. 58. Evaluate the integral of sin(x) dx. A) Sin(x) + C. B) Tan(x) + C. C) -sin(x) + C. D) -cos(x) + C. Show Answer Correct Answer: D) -cos(x) + C. 59. Find the antiderivative of $f(x) = e^x$ A) $\frac{e^x}{x} + C$. B) $xe^x + C$. C) $e^{x^2} + C$. D) $e^x + C$. Show Answer Correct Answer: D) $e^x + C$. 60. If in an exercise the function of the velocity is given:$v\left(t\right)$ A) Find the derivative of $v\left(t\right)$. B) Find the antiderivative of $v\left(t\right)$. C) Write random numbers and pray. D) Ask to my dog. Show Answer Correct Answer: B) Find the antiderivative of $v\left(t\right)$. 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