This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 7 Integrals – Quiz 8 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 8 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[2+\sqrt{3+\frac{4i}{n}}\right]\frac{4}{n}$ A) $\int_3^7\left(2+\sqrt{x}\right)dx$. B) $\int_0^4\left(2+\sqrt{x}\right)dx$. C) $\int_3^7\left(2x+\sqrt{x}\right)dx$. D) $\int_3^7\left(2+\sqrt{3+x}\right)dx$. Show Answer Correct Answer: A) $\int_3^7\left(2+\sqrt{x}\right)dx$. 2. $\int_1^2\int_0^2e^xdydx$ A) $e^2-e$. B) $2\left(e^2-e\right)$. C) $e^2$. D) $e^2-1$. Show Answer Correct Answer: B) $2\left(e^2-e\right)$. 3. $5\int_{ }^{ }\pi^xdx$ A) $\frac{5\pi}{\ln\left(x\right)}+C$. B) $\frac{5\pi^x}{\ln\left(\pi\right)}+C$. C) $\frac{5\pi^x}{\ln\left(5\right)}+C$. D) $\frac{5\pi^{\left(x+1\right)}}{x+1}+C$. Show Answer Correct Answer: B) $\frac{5\pi^x}{\ln\left(\pi\right)}+C$. 4. What is the antiderivative of $f(x) =\cos(x)$ A) $\sin(x) + C$. B) $-\sin(x) + C$. C) $\tan(x) + C$. D) $-\tan(x) + C$. Show Answer Correct Answer: A) $\sin(x) + C$. 5. Evaluate $\int\left(6\sqrt{x}-1\right)dx$ A) $4x^{\frac{3}{2}}-x+c$. B) 4x23-x+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $4x^{\frac{3}{2}}-x+c$. 6. How many Harry Potter movies are there? A) 5. B) 9. C) 8. D) 7. Show Answer Correct Answer: C) 8. 7. $\int_{ }^{ }\left(x+1\right)\left(2x-3\right)dx$ A) $\frac{2}{3}x^3-\frac{x^2}{2}-3x+c$. B) $\frac{2}{3}x^2-\frac{x}{2}-3+c$. C) $\left(\frac{x^2}{2}+x\right)\left(x^2-3x\right)+c$. D) $\frac{2}{3}x^3-\frac{x^2}{2}+3x+c$. Show Answer Correct Answer: A) $\frac{2}{3}x^3-\frac{x^2}{2}-3x+c$. 8. $\int\int x^2dydx$ A) $x^3y^3+C$. B) $\frac{1}{3}x^3y^3+C$. C) $\frac{1}{3}xy^3+C$. D) $\frac{1}{3}x^3y+C$. Show Answer Correct Answer: D) $\frac{1}{3}x^3y+C$. 9. Given F'(x) = x + 2 and F(0) = 3, find the particular solution for F(x). A) 1/2 x$^{2}$ + 2x + 3. B) 1/2 x$^{2}$ + 2x + 6. C) X$^{2}$ + 3. D) X$^{2}$ + 2x + 6. Show Answer Correct Answer: A) 1/2 x$^{2}$ + 2x + 3. 10. $\int_{ }^{ }4dx$ A) $0$. B) $4$. C) $4x+c$. D) $2x^2+c$. Show Answer Correct Answer: C) $4x+c$. 11. Let $A\left(x\right)=\int_0^x\sqrt{9-x^2}dx$ $A'\left(0\right)$ A) 3. B) 0. C) 9. D) -3. Show Answer Correct Answer: A) 3. 12. A particle moves along an axis so that at any time t>0, its velocity is given by v(t)=4-6t$^{2}$. If the particle is at position p=7 at t=1, what is the position of the particle at t=2? A) -10. B) -5. C) -3. D) 3. Show Answer Correct Answer: C) -3. 13. Evaluate $\int5x^4dx$ A) $x^5+c$. B) X5+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $x^5+c$. 14. What is the answer to page 4, #5? A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: B) B. 15. Calculate the average value of the function $f(x) = 4x$ $[1, 3]$ A) 4. B) 6. C) 8. D) 10. Show Answer Correct Answer: C) 8. 16. $\int_1^3\left(2-\frac{3}{x^2}\right)dx=$ A) 2. B) $-\frac{1}{2}$. C) $-2$. D) $0.5$. Show Answer Correct Answer: A) 2. 17. $\int\\frac{-2x}{\sqrt[]{-x^4+2x^2}}dx$ A) $\cos^{-1}\left(x^2-1\right)+c$. B) $\csc^{-1}\left(x^2\right)+c$. C) $\sqrt[]{-x^4+2x^2}+c$. D) $\sin^{-1}\left(1-x^2\right)+c$. Show Answer Correct Answer: A) $\cos^{-1}\left(x^2-1\right)+c$. 18. $\int_{ }^{ }\csc^2\left(x\right)dx$ A) $-\cot\left(x\right)+C$. B) $-\csc\left(x\right)+C$. C) $\cot\left(x\right)+C$. D) $\frac{\csc^3\left(x\right)}{3}+C$. Show Answer Correct Answer: A) $-\cot\left(x\right)+C$. 19. Find $\int(x^2+x+1)dx$ A) $x^3+x^2+x+c$. B) $\frac{1}{3}x^3+\frac{1}{2}x^2+x+c$. C) $\frac{1}{3}x^3+\frac{1}{2}x^2+x$. D) $x^3+x^2+x$. Show Answer Correct Answer: B) $\frac{1}{3}x^3+\frac{1}{2}x^2+x+c$. 20. For a function that is strictly decreasing, a right hand Riemann Sum is which of the following: A) Overestimate. B) Underestimate. C) Exact Solution. D) Unable to Determine. Show Answer Correct Answer: B) Underestimate. 21. Find the particular solution:f'(x) = 6x when f(-3) = 20 A) F(x)=3x-7. B) F(x)=3x$^{2}$-7. C) F(x)=3x$^{2}$ + 7. D) F(x)=3x$^{2}$ + 47. Show Answer Correct Answer: B) F(x)=3x$^{2}$-7. 22. $\int_0^2\int_0^{\infty}e^{-x}dxdy$ A) 2. B) 1. C) $e^2-1$. D) $e^{-2}-1$. Show Answer Correct Answer: A) 2. 23. Use $a\left(t\right)=-32\\frac{ft}{\sec^2}$ A) $1.75$. B) 1.75 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $1.75$. 24. $\int_1^3\left(x^2+1\right)dx$ A) $\frac{30}{3}$. B) $\frac{29}{3}$. C) $\frac{31}{3}$. D) $\frac{32}{3}$. Show Answer Correct Answer: D) $\frac{32}{3}$. 25. Evaluate $\int\sqrt{x}dx$ A) $x^{\frac{1}{2}}+C$. B) $\frac{1}{2}x^{-\frac{1}{2}}+C$. C) $x^{\frac{3}{2}}+C$. D) $\frac{2}{3}x^{\frac{3}{2}}+C$. Show Answer Correct Answer: D) $\frac{2}{3}x^{\frac{3}{2}}+C$. ← 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 4Class 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 9Class 12 Mathematics Chapter 7 Integrals Quiz 10Class 12 Mathematics Chapter 7 Integrals Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books