This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 7 Integrals – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 1 (25 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) $\int_1^{\infty}\left(2x-\sin x\right)dx$. B) $\int_{\frac{\pi}{4}}^{\infty}\left(2x-\sin x\right)dx$. C) $\int_1^{\infty}\left(2x-\sin\left(\frac{\pi}{4}\right)\right)dx$. D) $\int_0^{\frac{\pi}{4}}\left(2x-\sin x\right)dx$. Show Answer Correct Answer: D) $\int_0^{\frac{\pi}{4}}\left(2x-\sin x\right)dx$. 4. Which property of a graph will cause a left Riemann sum to be an overestimate? A) Increasing. B) Decreasing. C) Concave up. D) Concave down. Show Answer Correct Answer: B) Decreasing. 5. $\int_{ }^{ }f'\left(x\right)dx$ A) $f" \left(x\right)+C$. B) $f\left(\frac{x^2}{2}\right)+C$. C) $\frac{f^2\left(x\right)}{2}+C$. D) $f\left(x\right)+C$. Show Answer Correct Answer: D) $f\left(x\right)+C$. 6. $\int_{-1}^03e^xdx=$ A) $3-\frac{3}{e}$. B) $-\frac{3}{e}$. C) $3+3e$. D) $e^3-e$. Show Answer Correct Answer: A) $3-\frac{3}{e}$. 7. $\int_e^{e^3}\frac{2}{x}dx=$ A) 6. B) 5. C) 4. D) $e^6-2$. Show Answer Correct Answer: C) 4. 8. Another word for 'integral' is ..... A) Constant. B) Derivative. C) Antiderivative. D) Theorem. Show Answer Correct Answer: C) Antiderivative. 9. If $a\in R$ $\int_1^a\left(4x-1\right)dx=5$ $a= ..... $ A) $\frac{3}{2}$. B) 2. C) -2. D) $\frac{2}{3}$. E) 3. Show Answer Correct Answer: B) 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) 13. B) 15. C) 16. D) 17. E) 25. Show Answer Correct Answer: A) 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) 3. B) 6. C) 9. D) 27. Show Answer Correct Answer: D) 27. 14. $\int_{ }^{ }0dx$ A) $0$. B) $x+C$. C) $C$. D) $dx+C$. Show Answer Correct Answer: C) $C$. 15. Find the antiderivative off'(x) = x$^{2}$ when f(3) = 11. A) (1/3)x$^{3}$+ 2. B) X$^{3}$ + 29. C) (1/3)x$^{3}$ + 9. D) X$^{3}$ + 11. Show Answer Correct Answer: A) (1/3)x$^{3}$+ 2. 16. $\int_0^0\left(\sin x\right)dx$ A) 1. B) 2. C) 0. D) 4. Show Answer Correct Answer: C) 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) 26. C) 33. D) 66. Show Answer Correct Answer: C) 33. 18. $\int_{\frac{\pi}{4}}^{\pi}2\sin xdx$ A) $2+\sqrt{2}$. B) $-2-\sqrt{2}$. C) $2+\sqrt{3}$. D) $-2+2\sqrt{2}$. Show Answer Correct Answer: A) $2+\sqrt{2}$. 19. $\int_{-1}^1\left(2x-1\right)\left(2x+1\right)dx=$ A) 3. B) $-\frac{2}{3}$. C) $\frac{2}{3}$. D) $-1.5$. Show Answer Correct Answer: C) $\frac{2}{3}$. 20. Evaluate:$\int\left(\frac{2x^3+1}{x^2}\right)dx$ A) $x^2-\frac{1}{x}+C$. B) $\frac{2}{3}x^3+\frac{1}{x}+C$. C) $x^3-x^2+C$. D) $\frac{1}{2}x^2-\frac{1}{x}+C$. 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) 9. B) 12. C) 15. D) 18. Show Answer Correct Answer: B) 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) $\sum_{n=0}^8\left(2\left(1+0.5n\right)^2\right)$. C) $\sum_{n=1}^9\left(2\left(0.5n\right)^2\right)$. 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) $-\frac{1}{10}\left(3-2x\right)^5+c$. B) $\frac{\left(3-2x\right)^5}{10}+c$. C) $-10\left(3-2x\right)^5+c$. D) $\frac{\left(3-2x\right)^5}{5}+c$. Show Answer Correct Answer: A) $-\frac{1}{10}\left(3-2x\right)^5+c$. 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