This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 7 Integrals – Quiz 12 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 7 Integrals Quiz 12 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $\int_1^8\left(x^{\frac{1}{3}}+1\right)dx$ A) 1. B) 73/4. C) -87/4. D) 13/4. Show Answer Correct Answer: B) 73/4. 2. According to the Fundamental Theorem of Calculus, if $F$ $f$ $[a, b]$ $\int_a^b f(x) \, dx$ A) $F(b)-F(a)$. B) $F(a)-F(b)$. C) $F(b) + F(a)$. D) $F(a) + F(b)$. Show Answer Correct Answer: A) $F(b)-F(a)$. 3. If $\int_2^{10}f\left(x\right)dx=-6$ $\int_{10}^2f\left(x\right)dx$ A) -6. B) 6. C) 2. D) 10. Show Answer Correct Answer: B) 6. 4. Find the average value of the function $f\left(x\right)=x+3$ $\left[3, 9\right]$ A) $54$. B) $67.5$. C) $7.5$. D) $9$. Show Answer Correct Answer: D) $9$. 5. $\int\sin\left(x\right)dx$ A) $\cos\left(x\right)$. B) $\sin\left(x\right)$. C) $-\cos\left(x\right)$. D) $-\sin\left(x\right)$. Show Answer Correct Answer: C) $-\cos\left(x\right)$. 6. Given g(x) = x + 2 and G(0) = 3, find G(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. 7. What is the average value of $f\left(x\right)=\sqrt{4-x^2}$ $\left[0, 2\right]$ A) $\frac{\pi}{2}$. B) $\pi$. C) $2\pi$. D) $\frac{\pi}{4}$. Show Answer Correct Answer: A) $\frac{\pi}{2}$. 8. Which of the following is equivalent to:$\int_2^9f\left(\theta\right)d\theta-\int_4^9f\left(\theta\right)d\theta$ A) $\int_2^4f\left(\theta\right)d\theta$. B) $\int_4^2f\left(\theta\right)d\theta$. C) $\int_2^7f\left(\theta\right)d\theta$. D) None of the following are equivalent to the given. Show Answer Correct Answer: A) $\int_2^4f\left(\theta\right)d\theta$. 9. Evaluate the following definite integral via u-substitution $\int_0^118x^2\left(2x^3+1\right)^2dx$ A) $26$. B) $1$. C) $\frac{26}{3}$. D) $\frac{1}{3}$. Show Answer Correct Answer: A) $26$. 10. Integration is the inverse of differentiation but it applications it can be used to ..... A) Find the area under a curve. B) Calculate the force of an object. C) Find the altitude of an objects perimeter. D) None of the above. Show Answer Correct Answer: A) Find the area under a curve. 11. Find the area under a curve defined by the equation 5x$^{4}$+3x+7 between the x values 0 and 4. A) 1200. B) 1/12. C) 1134. D) 1076. Show Answer Correct Answer: D) 1076. 12. What is the area under the curve of $y = 4-x^2$ $x =-2$ $x = 2$ A) 16/3. B) 32/3. C) 8. D) 16. Show Answer Correct Answer: B) 32/3. 13. $\int_1^2\int_3^4\left(2x-7y\right)dxdy$ A) 3.50. B) -3.50. C) 1.50. D) -1.50. Show Answer Correct Answer: B) -3.50. 14. Evaluate $\int e^xdx$ A) $2e^{2x}+C$. B) $e^{2x^2}+C$. C) $e^{\frac{1}{2}x^2}+C$. D) $e^x+C$. Show Answer Correct Answer: D) $e^x+C$. 15. Calculate the average value of the function $f(x) = 2x + 3$ $[1, 4]$ A) $\frac{5}{2}$. B) 5. C) $\frac{11}{2}$. D) 11. Show Answer Correct Answer: C) $\frac{11}{2}$. 16. $\int\\frac{6x+5}{\sqrt[]{x}}dx$ A) $\frac{9}{\sqrt[]{x^3}}+c$. B) $4\\sqrt[]{x^3}+10\\sqrt[]{x}+c$. C) $\frac{3}{\sqrt[]{x}}-\frac{5}{2\\sqrt[]{x^3}}+c$. D) $9\\sqrt[]{x^3}+\frac{5}{2}\\sqrt[]{x}+c$. Show Answer Correct Answer: B) $4\\sqrt[]{x^3}+10\\sqrt[]{x}+c$. 17. Find the antiderivative:$\int_{ }^{ }5x^6dx$ A) $x^6$. B) $x^6+C$. C) $\frac{5x^7}{7}$. D) $\frac{5x^7}{7}+C$. Show Answer Correct Answer: D) $\frac{5x^7}{7}+C$. 18. Find the area under the curve y =3x$^{2}$-2x from x= 1 to x =5. A) 100. B) 99. C) 150. D) 152. Show Answer Correct Answer: A) 100. 19. $\int\left(\pi+3\sqrt{x}^{ }\right)dx$ A) $\pi x+2\sqrt{x^3}+c$. B) $\frac{\pi^2}{2}+2\sqrt{x^3}+c$. C) $\pi x+\frac{3}{2}\sqrt{x}+c$. D) $\pi+\frac{2}{3}\sqrt{x}+c$. Show Answer Correct Answer: A) $\pi x+2\sqrt{x^3}+c$. 20. $\int_1^2\left(2x+k\right)dx=8.$ $\k=?$ A) $4$. B) $5$. C) $-3$. D) $-2$. Show Answer Correct Answer: B) $5$. 21. $\int\left(\frac{1}{x^3}\right)dx$ A) Ln| $x^3$. B) $\frac{1}{x^2}$. C) $-\frac{3}{x^4}$. D) $-\frac{1}{2x^2}+C$. Show Answer Correct Answer: D) $-\frac{1}{2x^2}+C$. 22. Set up limit of triple integral to find the volume of the solid that lies below the hemisphere $z=\sqrt{25-x^2-y^2}$ $x^2+y^2=16$ $x^2+y^2=25$ A) $\int_0^{2\pi}\int_0^4\int_0^{\sqrt{25-r^2}}rdzdrd\theta$. B) $\int_0^{2\pi}\int_0^5\int_0^{\sqrt{25-r^2}}rdzdrd\theta$. C) $\int_0^{2\pi}\int_4^5\int_0^{\sqrt{25-r^2}}rdzdrd\theta$. D) $\int_0^{2\pi}\int_4^5\int_0^5rdzdrd\theta$. Show Answer Correct Answer: C) $\int_0^{2\pi}\int_4^5\int_0^{\sqrt{25-r^2}}rdzdrd\theta$. 23. $\int\frac{1}{\sqrt{1-x^2}}dx$ A) $2\sqrt{1-x^2}+C$. B) $-4x\sqrt{1-x^2}+C$. C) $\arccos\left(x\right)+C$. D) $\arcsin\left(x\right)+C$. Show Answer Correct Answer: D) $\arcsin\left(x\right)+C$. 24. Integrate $\frac{1}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ A) $-\left(1+\frac{1}{x^4}\right)^{\frac{1}{4}}$. B) $\left(x^4+1\right)^{\frac{1}{4}}$. C) $-\left(1+\frac{1}{x^4}\right)^{\frac{3}{4}}$. D) None of the above. Show Answer Correct Answer: A) $-\left(1+\frac{1}{x^4}\right)^{\frac{1}{4}}$. 25. $\int_{ }^{ }\\frac{4}{\sqrt{x}}dx$ A) $8\sqrt{x}+C$. B) $2\sqrt{x}+C$. C) $\frac{4x}{\sqrt{x}}+C$. D) None of these. Show Answer Correct Answer: A) $8\sqrt{x}+C$. ← PreviousRelated 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