This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 7 Integrals – Quiz 6 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 6 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the antiderivative of $f(x) = \frac{1}{x}$ A) $\ln|x| + C$. B) $e^x + C$. C) $\frac{1}{2}x^2 + C$. D) $x\ln(x)-x + C$. Show Answer Correct Answer: A) $\ln|x| + C$. 2. Evaluate the indefinite integral. $\int_{ }^{ }\left(2x+2x^{-3}-6x^{-4}\right)dx$ A) $x-x^{-3}+2x^4+C$. B) $-2x+C$. C) $x^2-x^{-2}+2x^{-3}+C$. D) $2x^2+2x^{-2}-6x^{-3}+C$. Show Answer Correct Answer: C) $x^2-x^{-2}+2x^{-3}+C$. 3. $\int_0^3g\left(x\right)dx=-5$ $\int_3^02g\left(x\right)dx=$ A) $-10$. B) $10$. C) $-7$. D) $-\frac{5}{2}$. Show Answer Correct Answer: B) $10$. 4. $\int_0^{\pi/2}\int_0^{\pi/2}\cos\theta\cos\varphi d\theta d\varphi$ A) 1. B) 0. C) $\pi$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: A) 1. 5. Which of the following is the solution to the differential equation dy/dx = e$^{y+x}$ with the initial condition y(0) =-ln 4? A) Y =-x-ln 4. B) Xy = x-ln 4. C) Y =-ln(-e$^{x}$ + 5). D) Y =-ln(e$^{x}$ + 3). E) Y = ln(e$^{x}$ + 3). Show Answer Correct Answer: C) Y =-ln(-e$^{x}$ + 5). 6. $\int\left(\frac{1}{x^2}+\frac{6}{x^3}\right)dx$ A) $-x^{-1}-3x^{-2}+C$. B) $\frac{x^{-3}}{-3}+\frac{6x^{-4}}{-4}+C$. C) $-x^{-1}-3x^{-2}$. D) $-x-3x^2+C$. Show Answer Correct Answer: A) $-x^{-1}-3x^{-2}+C$. 7. The integration of f(x)= 1/tan(x) dx is:HINT:What is 1/tan(x) the same as? A) -ln Icos(x)I + C. B) Ln Isin(x)I +C. C) Sec$^{2}$ (x) + C. D) -ln Isin(x)I +C. Show Answer Correct Answer: B) Ln Isin(x)I +C. 8. The percentage of error using the trapezoidal rule with 3 strips for $\int_0^3x\left(3-x\right)dx$ A) 10%. B) 12%. C) 9%. D) 11%. Show Answer Correct Answer: D) 11%. 9. $\int_{ }^{ }\\frac{1}{a^2+x^2}dx=$ A) $\frac{1}{a}\arcsin\\frac{x}{a}+C$. B) $\frac{1}{a}\arctan\\frac{x}{a}+C$. C) $\arctan\\frac{x}{a}+C$. D) $\arcsin\\frac{x}{a}+C$. Show Answer Correct Answer: B) $\frac{1}{a}\arctan\\frac{x}{a}+C$. 10. In $\int_0^1\int_0^{1-z}\int_0^{1-y-z}xyzdxdydz$ A) 0 to 1. B) 0 to 1-z. C) 0 to 1-y-z. D) 1 to 1-y-z. Show Answer Correct Answer: C) 0 to 1-y-z. 11. $\int_{ }^{ }-24x^5\\dx$ A) $-6x^4+C$. B) $-4x^5+C$. C) $-4x^6+C$. D) $-24x^6+C$. Show Answer Correct Answer: C) $-4x^6+C$. 12. $\int_0^{\\pi}\sin\left(x\right)\\dx$ A) -2. B) 1. C) -1. D) 0. E) 2. Show Answer Correct Answer: E) 2. 13. Find the average value of $f\left(x\right)=6-2x$ $\left[-1, 4\right]$ A) 3. B) 3.2. C) 10. D) 15. Show Answer Correct Answer: A) 3. 14. Single integral gives the area under a curve. A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 15. Evaluate:$\int_4^{\infty}\frac{-2x}{\left(9-x^2\right)^{\frac{1}{3}}}dx$ A) $7^{\frac{2}{3}}$. B) $\frac{3}{2}\cdot7^{\frac{2}{3}}$. C) $9^{\frac{2}{3}}+7^{\frac{2}{3}}$. D) $\frac{3}{2}\left(9^{\frac{2}{3}}+7^{\frac{2}{3}}\right)$. E) Diverges. Show Answer Correct Answer: E) Diverges. 16. $\int\int\left(y-z\right)dxdy$ A) $\frac{1}{2}xy^2-xyz+C$. B) $\frac{1}{2}xy^2+xyz+C$. C) $\frac{1}{2}x^2y^{ }-xyz+C$. D) $\frac{1}{2}xy^2-x^2yz+C$. Show Answer Correct Answer: A) $\frac{1}{2}xy^2-xyz+C$. 17. $\int_{ }^{ }\\dy$ A) $y+C$. B) $1+C$. C) $\frac{1}{2}y^2+C$. D) $x+C$. Show Answer Correct Answer: A) $y+C$. 18. Integral of $\frac{1}{e^x+e^{-x}}$ A) $\tan^{-1}\left(e^{-x}\right)+C$. B) $\tan^{-1}\left(e^x\right)+C$. C) $\log\left(e^x-e^{-x}\right)+C$. D) $\log\left(e^x+e^{-x}\right)+C$. Show Answer Correct Answer: B) $\tan^{-1}\left(e^x\right)+C$. 19. $\int_{-a}^a\left(2\sin2x\right)dx$ A) 2a. B) -a. C) -2a. D) 0. Show Answer Correct Answer: D) 0. 20. $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{5i}{n}\right)^2+\frac{5i}{n}+1\right]\frac{5}{n}$ A) $\int_0^5\left(x^2+x+1\right)dx$. B) $\int_5^6\left(x^2+x+1\right)dx$. C) $\int_0^1\left(\left(5x\right)^2+5x+1\right)dx$. D) $\int_0^{10}\left(\frac{x^2}{2}+\frac{x}{2}+1\right)dx$. Show Answer Correct Answer: A) $\int_0^5\left(x^2+x+1\right)dx$. 21. What is the answer to page 7, #1? A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: B) B. 22. $\int_{ }^{ }9\sin\left(3x\right)dx$ A) $27\cos\left(3x\right)+C$. B) $3\cos\left(3x\right)+C$. C) $-3\cos\left(3x\right)+C$. D) $-27\cos\left(3x\right)+C$. Show Answer Correct Answer: C) $-3\cos\left(3x\right)+C$. 23. $\int_1^3\left(4-2x\right)dx=$ A) 0. B) $-\frac{5}{2}$. C) $\frac{2}{5}$. D) $-0.4$. E) 6. Show Answer Correct Answer: A) 0. 24. How do you get from the first derivative the the original function? A) Differentiate. B) Integrate. C) All the above. D) None of the above. Show Answer Correct Answer: B) Integrate. 25. Evaluate the definite integral $\int_1^e \frac{1}{x} \, dx$ A) 1. B) E. C) $\ln(e)$. D) $e-1$. Show Answer Correct Answer: A) 1. ← 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 4Class 12 Mathematics Chapter 7 Integrals Quiz 5Class 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