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CBSE - Class 12 > Mathematics > Integrals Worksheets

Free CBSE - Class 12 Mathematics - Integrals worksheets

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Here is a Sample Worksheet for you to Practice. Download this worksheet to see the answers.

1.
Prove the following (Exercises 32 to 37)
33. $\int_{0}^{1} x e^x dx = 1$
2.
Prove the following (Exercises 32 to 37)
34. $\int_{-1}^{1} x^{17} \cos^4 x dx = 0$
3.
Prove the following (Exercises 32 to 37)
35. $\int_{0}^{\frac{\pi}{2}} \sin^3 x dx = \frac{2}{3}$
4.
Prove the following (Exercises 32 to 37)
36. $\int_{0}^{\frac{\pi}{4}} 2\tan^3 x dx = 1 - \log 2$
5.
Prove the following (Exercises 32 to 37)
37. $\int_{0}^{1} \sin^{-1} x dx = \frac{\pi}{2} - 1$
6.
Choose the correct answers in Exercises 38 to 40
38. $\int \frac{dx}{e^x + e^{-x}}$ is equal to
1. $\tan^{-1}(e^x) + C$ 2. $\tan^{-1}(e^{-x}) + C$ 3. $\log(e^x - e^{-x}) + C$ 4. $\log(e^x + e^{-x}) + C$
7.
Choose the correct answers in Exercises 38 to 40
39. $\int \frac{\cos 2x}{(\sin x + \cos x)^2} dx$ is equal to
1. $\frac{-1}{\sin x + \cos x} + C$ 2. $\log |\sin x + \cos x| + C$ 3. $\log |\sin x - \cos x| + C$ 4. $\frac{1}{(\sin x + \cos x)^2}$
8.
Choose the correct answers in Exercises 38 to 40
40. If $f(a+b-x) = f(x)$, then $\int_{a}^{b} x f(x) dx$ is equal to
1. $\frac{a+b}{2} \int_{a}^{b} f(b-x) dx$ 2. $\frac{a+b}{2} \int_{a}^{b} f(b+x) dx$ 3. $\frac{b-a}{2} \int_{a}^{b} f(x) dx$ 4. $\frac{a+b}{2} \int_{a}^{b} f(x) dx$
9.
Evaluate the definite integrals in Exercises 24 to 31.
31. $\int_{1}^{4} [|x-1|+|x-2|+|x-3|] dx$
10.
Prove the following (Exercises 32 to 37)
32. $\int_{1}^{3} \frac{dx}{x^2(x+1)} = \frac{2}{3} + \log \frac{2}{3}$
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Chapters in CBSE - Class 12 Mathematics

Application of Derivatives Worksheet Application of Integrals Worksheet Continuity and Differentiability Worksheet Determinants Worksheet Differential Equations Worksheet Inverse Trigonometric Functions Worksheet Linear Programming Worksheet Matrices Worksheet Probability Worksheet Relations and Functions Worksheet Three Dimensional Geometry Worksheet Vector Algebra Worksheet

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