This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 7 Integrals – Quiz 11 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 11 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. For a function that is strictly increasing, a right hand Riemann Sum is which of the following: A) Overestimate. B) Underestimate. C) Unable to Determine. D) Exact Solution. Show Answer Correct Answer: A) Overestimate. 2. Ten years ago, a school with a fixed population decided to increase the size of its student body. The size of the student body t years since the increase began is given as s(t). It is known that the value of the definite integral from 0 to 10 of s'(t) is 400. Which is true? A) The student body is now at 400. B) The student body is increasing by 400 per year. C) The student body grew by 400 students. D) Nothing can be determined from this information. Show Answer Correct Answer: C) The student body grew by 400 students. 3. True or false:since every function has a derivative, every function has an antiderivative. A) True. B) False. C) Eh well, uh I mean . D) None of the above. Show Answer Correct Answer: C) Eh well, uh I mean . 4. Given that the demand function D(x) and the supply function S(x) of a product are given as $D(x)=12-x$ $S\left(x\right)=x+6$ A) RM4.50. B) RM9. C) RM3. D) RM2.50. Show Answer Correct Answer: A) RM4.50. 5. Evaluate:$\int e^{2x}dx$ A) $e^{2x}+C$. B) $e^{3x}+C$. C) $2e^{2x}+C$. D) $\frac{1}{2}e^{2x}+C$. Show Answer Correct Answer: D) $\frac{1}{2}e^{2x}+C$. 6. Evaluate the indefinite integral. $\int\left(4\csc x\cot x-6\cos x\right)dx$ A) $-4\csc x-6\sin x+C$. B) $-4\csc x+6\sin x+C$. C) $4\cot x-6\sin x+C$. D) $4\csc x+6\sin x+C$. Show Answer Correct Answer: A) $-4\csc x-6\sin x+C$. 7. Integrate the following indefinite integral via u-substitution $\int_{ }^{ }\left(2+2x\right)e^{\left(4x+2x^2\right)}dx$ A) $\frac{1}{2}e^{\left(4x+2x^2\right)}+C$. B) $2e^{\left(4x+2x^2\right)}+C$. C) $e^{2\left(4x+2x^2\right)}+C$. D) $e^{\frac{1}{2}\left(4x+2x^2\right)}+C$. Show Answer Correct Answer: A) $\frac{1}{2}e^{\left(4x+2x^2\right)}+C$. 8. What is the relationship between the derivative and the integral? A) The derivative is a type of integral. B) The integral measures the rate of change. C) The derivative and the integral are inverse operations. D) The derivative and the integral are unrelated concepts. Show Answer Correct Answer: C) The derivative and the integral are inverse operations. 9. $\int\sqrt{x^5}dx= ..... $ A) $\frac{7}{2}\sqrt{x^7}+c$. B) $\frac{2}{7}\sqrt{x^7}+c$. C) $\frac{7}{2\sqrt{x^7}}+c$. D) $\frac{2}{7\sqrt{x^7}}+c$. Show Answer Correct Answer: B) $\frac{2}{7}\sqrt{x^7}+c$. 10. The integral 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. 11. $\int_{ }^{ }8\left(1+2x\right)^{-3}dx=\frac{-2}{\left(1+2x\right)^2}+c$ A) CORRECT/ BETUL. B) WRONG/ SALAH. C) All the above. D) None of the above. Show Answer Correct Answer: A) CORRECT/ BETUL. 12. $\cot^3x$ A) LogIcosecxI-cosec x. B) $\log\operatorname{cosec}x-\frac{\operatorname{cosec}^2x}{2}$. C) $\log\\cot x\-\\frac{\operatorname{cosec}^2x}{2}$. D) None of the above. Show Answer Correct Answer: B) $\log\operatorname{cosec}x-\frac{\operatorname{cosec}^2x}{2}$. 13. Trapezozidal rule is NOT the method of finding the exact value of a definite integral.This statement is A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 14. $\frac{\cos x}{\left(1+\sin x\right)\left(2+\sin x\right)}$ A) $\log\left(1+\sin x\right)\left(2+\sin x\right)$. B) $\log\frac{2+\sin x}{1+\sin x}$. C) $\log\frac{\left(1+\sin x\right)}{2+\sin x}$. D) None of the above. Show Answer Correct Answer: C) $\log\frac{\left(1+\sin x\right)}{2+\sin x}$. 15. Triple integrals give: A) Mass only. B) Mass & volume. C) Headache. D) Heart attack. Show Answer Correct Answer: B) Mass & volume. 16. If $\int_2^{10}f\left(x\right)dx=-6$ $\int_2^{10}\\frac{1}{3}f\left(x\right)dx$ A) 2. B) 18. C) -2. D) -18. Show Answer Correct Answer: C) -2. 17. Given v(t) = x$^{-9}$, find the general equation for the antiderivative. A) (1/8)x$^{-8}$ + C. B) (-1/8)x$^{-8 }$+ C. C) (1/10)x$^{10}$. D) (-1/8)x$^{-8}$. Show Answer Correct Answer: B) (-1/8)x$^{-8 }$+ C. 18. $\int_1^35x^2dx$ A) 43. B) 130/3. C) 40. D) 19/3. Show Answer Correct Answer: B) 130/3. 19. Evaluate $\int\left(x^{-1}-1\right)dx$ A) $\ln x-x+c$. B) Lnx-x+c Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $\ln x-x+c$. 20. $\int\frac{1}{x}dx$ A) Ln|x| + C. B) $-\frac{1}{x^2}$. C) $\frac{1}{x^2}$. D) 1 + C. Show Answer Correct Answer: A) Ln|x| + C. 21. What is the area between the curve $y=-3x^2+12$ $x=0$ $x=2$ A) 12. B) 16. C) 24. D) 32. Show Answer Correct Answer: B) 16. 22. Determine the rule we follow to find the antiderivative of $x^n.$ A) $nx^{\left(n-1\right)}+C$. B) $\left(n+1\right)n^{\left(n+1\right)}+C$. C) $\frac{1}{n-1}x^{\left(n-1\right)}+C$. D) $\frac{x^{\left(n+1\right)}}{n+1}+C$. Show Answer Correct Answer: D) $\frac{x^{\left(n+1\right)}}{n+1}+C$. 23. Find $\int(12x^3-4x)dx$ A) $3x^4-2x^2+c$. B) $3x^4-4x^2+c$. C) $4x^3-2x+c$. D) $12x^4-x^2+c$. Show Answer Correct Answer: A) $3x^4-2x^2+c$. 24. The area under a curve is also known as the ..... ? A) Physical area. B) Algebraic area. C) Integral. D) Antiderivative. Show Answer Correct Answer: A) Physical area. 25. Evaluate the definite integral $\int_0^4 2x \, dx$ A) 8. B) 16. C) 4. D) 32. Show Answer Correct Answer: B) 16. ← 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 8Class 12 Mathematics Chapter 7 Integrals Quiz 9Class 12 Mathematics Chapter 7 Integrals Quiz 10 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books