This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 7 Integrals – Quiz 5 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 5 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the answer to page 3, #2? A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: C) C. 2. 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. 3. $\int_{ }^{ }\left(2x-1\right)^2dx$ A) $\frac{4x^3}{3}-2x^2+x+c$. B) $\frac{4}{3}x^3-x^2+x+c$. C) $\left(x^2-x\right)^2+c$. D) $\frac{\left(2x-1\right)^3}{3}+c$. Show Answer Correct Answer: A) $\frac{4x^3}{3}-2x^2+x+c$. 4. The integral represents ..... A) A variable. B) A derivative. C) The area under a curve. D) When you have integrity. Show Answer Correct Answer: C) The area under a curve. 5. Using the Fundamental Theorem of Calculus, evaluate $\int_{0}^{2} 3x^2 dx$ A) 4. B) 8. C) 12. D) 16. Show Answer Correct Answer: C) 12. 6. 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. 7. $\int_{ }^{ }\frac{e^3}{5}dx$ A) $\frac{e^4}{20}+C$. B) $\frac{e^4}{9}+C$. C) $\frac{3e^3}{5}+C$. D) $\frac{xe^3}{5}+C$. Show Answer Correct Answer: D) $\frac{xe^3}{5}+C$. 8. What is the solution of $\int_0^3\left(3x^2\right)dx$ A) 21. B) 23. C) 25. D) 27. Show Answer Correct Answer: D) 27. 9. There are ..... cases of L'Hopital's rule. A) 2. B) 5. C) 7. D) 8. Show Answer Correct Answer: C) 7. 10. What is the answer to page 5, #7? A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: E) E. 11. $\int_{ }^{ }\frac{\pi}{x}dx$ A) $\frac{\pi x}{0}+C$. B) $\pi\ln\left(x\right)+C$. C) $\ln\left(\frac{\pi}{x}\right)+C$. D) $\frac{\ln\left(\pi\right)}{x}+C$. Show Answer Correct Answer: B) $\pi\ln\left(x\right)+C$. 12. $\frac{d}{dx}\left(\sin^{-1}x\right)$ A) $\cos^{-1}x$. B) $-\cos^{-1}x$. C) $-\frac{1}{\sqrt{1-x^2}}$. D) $\frac{1}{\sqrt{1-x^2}}$. Show Answer Correct Answer: D) $\frac{1}{\sqrt{1-x^2}}$. 13. What is the area of the region enclosed by the graphs of f(x)=x-2x$^{2}$ and g(x)=-5x? A) 7/3. B) 16/3. C) 20/3. D) 9. Show Answer Correct Answer: D) 9. 14. $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\left(1+\sin3t\right)\left(\cos3t\right)dt=$ A) 0. B) 1/2. C) -1/2. D) 1. Show Answer Correct Answer: C) -1/2. 15. $\int_0^2\int_0^yx^2dxdy$ A) $\frac{2}{3}$. B) $\frac{4}{3}$. C) $\frac{1}{3}$. D) $\frac{5}{3}$. Show Answer Correct Answer: B) $\frac{4}{3}$. 16. Calculate the definite integral of 3x from 1 to 4. A) 30. B) 22.5. C) 15. D) 10. Show Answer Correct Answer: B) 22.5. 17. Evaluate:$\int_2^{\infty}\frac{1}{x^2}dx$ A) $\frac{1}{2}$. B) $\ln2$. C) $1$. D) $3$. E) Diverges. Show Answer Correct Answer: A) $\frac{1}{2}$. 18. 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. 19. $\int_{ }^{ }x^3dx$ A) $\frac{1}{4}x^4+c$. B) $x^4+c$. C) $\frac{1}{3}x^3+c$. D) $3x^2+c$. Show Answer Correct Answer: A) $\frac{1}{4}x^4+c$. 20. $\int_0^{\pi}24\sin\left(6x\right)\cos\left(6x\right)dx=$ A) -8/3. B) -4/3. C) 0. D) 4/3. Show Answer Correct Answer: C) 0. 21. $\int_{ }^{ }\left[5^x-\csc^2x\right]dx$ A) $5^x-\cot x+C$. B) $5^x+\cot x+C$. C) $\frac{5^x}{\ln5}+\cot x+C$. D) $\frac{5^x}{\ln x}-\cot x+C$. Show Answer Correct Answer: C) $\frac{5^x}{\ln5}+\cot x+C$. 22. Evaluate $\int_{ }^{ }x^{\frac{1}{3}}dx$ A) $\frac{3x^{\frac{4}{3}}}{4}+c$. B) 43x34+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\frac{3x^{\frac{4}{3}}}{4}+c$. 23. $\int_2^5\left(x^3+3\right)dx$ A) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{1}{n}$. B) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3i}{n}$. C) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$. D) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$. Show Answer Correct Answer: D) $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3}{n}$. 24. $\int_0^{\frac{\pi}{2}}\int_0^1rdrd\theta$ A) 0. B) 1. C) $\frac{\pi}{4}$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: C) $\frac{\pi}{4}$. 25. Calculate the average value of the function $f(x) = x^2$ $[0, 2]$ A) $\frac{2}{3}$. B) $\frac{4}{3}$. C) 2. D) 3. Show Answer Correct Answer: B) $\frac{4}{3}$. ← 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 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