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CBSE - Class 12 > Mathematics > Integrals Worksheets

Free CBSE - Class 12 Mathematics - Integrals worksheets

Sample Worksheets

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.
Integrate the functions in Exercises 1 to 23.
16. $e^{3\log x} (x^4+1)^{-1}$
10.
Integrate the functions in Exercises 1 to 23.
17. $f'(ax+b)[f(ax+b)]^n$
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Chapters in CBSE - Class 12 Mathematics

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

Free Integrals Worksheets

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