This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 7 Integrals – Quiz 4 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 4 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. 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) $\int_5^9g\left(w\right)dw$. 2. $\int_1^5\left(-x^2+6x-10\right)dx$ A) $\frac{28}{3}$. B) $\frac{-28}{3}$. C) 28. D) $-\frac{7}{2}$. Show Answer Correct Answer: B) $\frac{-28}{3}$. 3. What is the answer to page 3, #1? A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: B) B. 4. What is the antiderivative of $f(x) = 6x$ A) $3x^2 + C$. B) $6x^2 + C$. C) $x^6 + C$. D) $12x + C$. Show Answer Correct Answer: A) $3x^2 + C$. 5. 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) $-x^{-1}-3x^{-2}+c$. 6. The area of the region bounded by the curve y = x$^{2}$ and the line y = 16 A) 32/3. B) 256/3. C) 64/3. D) 128/3. Show Answer Correct Answer: B) 256/3. 7. $\int_0^2\int_0^{z^2}\int_0^{\left(y-z\right)}\left(2x-y\right)dxdydz$ A) $\frac{14}{15}$. B) $1$. C) $\frac{13}{15}$. D) $\frac{16}{15}$. Show Answer Correct Answer: D) $\frac{16}{15}$. 8. $\int\left(\sqrt{x}^{ }+4e^{4x}+5\right)dx$ A) $x^{\frac{3}{2}}+e^{4x}+5x+c$. B) $\frac{2}{3}x^{\frac{3}{2}}+e^{4x}+5x+c$. C) $\sqrt{x}+e^{4x}+5x+c$. D) $\frac{2}{3}x^{\frac{3}{2}}+4e^{4x}+5x+c$. Show Answer Correct Answer: B) $\frac{2}{3}x^{\frac{3}{2}}+e^{4x}+5x+c$. 9. 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. 10. Evaluate $\int7x-9x_{ }^{-3}-2\\dx$ A) $F\left(x\right)=7+27x^{-4}+C$. B) $F\left(x\right)=\frac{7}{2}x^2+\frac{9}{2}x^{-2}-2x+C$. C) $F\left(x\right)=7x^2-9x^{-2}-2x+C$. D) $F\left(x\right)=7x^0-9x^{-4}-2x^{-1}+C$. Show Answer Correct Answer: B) $F\left(x\right)=\frac{7}{2}x^2+\frac{9}{2}x^{-2}-2x+C$. 11. $\int_0^{\pi/2}\int_0^1\cos ydxdy$ A) 1. B) 2. C) 0. D) -1. Show Answer Correct Answer: A) 1. 12. What is the meaning of the following symbol:$\int_a^bf\left(x\right)dx$ A) The area from the curve to the x-axis from x = a to x = b. B) The rate at which f(x) is changing 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: A) The area from the curve to the x-axis from x = a to x = b. 13. 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) There is no c on [0, 4] that satisfies the MVT for integrals. C) $\frac{\pi}{4}$. D) $\frac{-\pi}{4}$. Show Answer Correct Answer: A) 0. 14. $\int_0^1\int_0^xf\left(x, y\right)dydx=_{ }$ A) $\int_y^1\int_0^1xydxdy$. B) $\int_0^x\int_0^1f\left(x, y\right)dydx$. C) $\int_0^1\int_y^1f\left(x, y\right)dxdy$. D) $\int_1^0\int_x^0f\left(x, y\right)dydx$. Show Answer Correct Answer: C) $\int_0^1\int_y^1f\left(x, y\right)dxdy$. 15. The integration of f(x)= 1/x dx A) Ln IxI + C. B) X$^{2}$ /2. C) -x$^{2}$/2. D) -2x$^{2}$. Show Answer Correct Answer: A) Ln IxI + C. 16. $\int\int\left(3x^2+2y\right)dxdy$ A) $xy\left(y^2+x\right)+C$. B) $xy\left(x^2+y\right)+C$. C) $x^3y^2+xy^2+C$. D) $x^2y^3+xy+C$. Show Answer Correct Answer: B) $xy\left(x^2+y\right)+C$. 17. The equal double integral in polar co-ordinates of $\int_0^{\infty}\int_0^{\infty}e^{-(x^2+y^2)}dxdy$ A) $\int_0^{\pi/2}\int_0^{\infty}e^{-r^2}rdrd\theta$. B) $\int_0^{\pi/2}\int_0^1e^{-r^2}drd\theta$. C) $\int_0^{\infty}\int_0^{\infty}e^{-r^2}drd\theta$. D) $\int_0^{\infty}\int_0^{\infty}e^{-(r^2+\theta^2)}drd\theta$. Show Answer Correct Answer: A) $\int_0^{\pi/2}\int_0^{\infty}e^{-r^2}rdrd\theta$. 18. Evaluate $\int_0^3\frac{dx}{x-2}$ A) Diverges. B) Ln(1/2). C) Ln1-ln2. D) -0.693. Show Answer Correct Answer: A) Diverges. 19. 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) 3 sq. units. D) 1 sq. units. Show Answer Correct Answer: D) 1 sq. units. 20. $\int_{ }^{ }\\sec^2\left(x\right)dx$ A) $\tan\left(x\right)+C$. B) $\sec\left(x\right)\tan\left(x\right)+C$. C) $\tan^2\left(x\right)+C$. D) $\frac{1}{3}\sec^3\left(x\right)+C$. Show Answer Correct Answer: A) $\tan\left(x\right)+C$. 21. $2\pi\int_0^1\left(y+1\right)\sqrt{1-y}dy$ A) $\frac{14}{15}$. B) $\frac{-28\pi}{15}$. C) $\frac{-14}{15}$. D) $\frac{28\pi}{15}$. Show Answer Correct Answer: D) $\frac{28\pi}{15}$. 22. $\int\\sin\left(4x-5\right)dx$ A) $-\frac{1}{4}\cos\left(4x-5\right)+c$. B) $4\cos\left(4x-5\right)+c$. C) $-\cos\left(4x-5\right)+c$. D) $\frac{1}{4}\sin\left(4x-5\right)+c$. Show Answer Correct Answer: A) $-\frac{1}{4}\cos\left(4x-5\right)+c$. 23. What is the area under the curve of $y = x^2$ $x = 1$ $x = 3$ A) $\frac{26}{3}$. B) $\frac{28}{3}$. C) 9. D) $\frac{20}{3}$. Show Answer Correct Answer: A) $\frac{26}{3}$. 24. Find the enclosed area by the curve with equation $y=4-x^2$ A) 5. B) 7. C) 9. D) 11. Show Answer Correct Answer: C) 9. 25. Integrate $\int_{ }^{ }x^{\frac{1}{3}}dx$ A) $=\frac{4}{3}x^{\frac{4}{3}}+c$. B) $=\frac{3}{2}x^{\frac{2}{3}}+c$. C) $=\frac{1}{3}x^{-\frac{2}{3}}+c$. D) $=\frac{3}{4}x^{\frac{4}{3}}+c$. Show Answer Correct Answer: D) $=\frac{3}{4}x^{\frac{4}{3}}+c$. ← PreviousNext →Related 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 7 Integrals Quiz 6Class 12 Mathematics Chapter 7 Integrals Quiz 7Class 12 Mathematics Chapter 7 Integrals Quiz 8Class 12 Mathematics Chapter 7 Integrals Quiz 9Class 12 Mathematics Chapter 7 Integrals Quiz 10Class 12 Mathematics Chapter 7 Integrals Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books