Dr.Harswaroop Sharma Mathematics Solution Class 12 Chapter 7 समाकलन (Integration) Exercise 7D

    

प्रश्नावली - 7D

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Question 1

निम्नलिखित समाकलों के मान क्ञात कीजिए-
1. $\int \sin \left(2 x+\frac{\pi}{2}\right) d x$.

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Question 2

2. $\int x^3 \cos x^4 d x$.

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Question 3

3. $\int(4 x+2) \sqrt{x^2+x+1} d x$.

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Question 4

4. $\int n x^{n-1} \cos x^n d x$.

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Question 5

5. $\int \frac{1}{x(\log x)^m} d x$.

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Question 6

6. $\int \frac{x}{\sqrt{1-x^4}} d x$.

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Question 7

7. $\int \frac{x}{1+x^4} d x$.

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Question 8

8. $\int \frac{x d x}{\sqrt{1+x^2}}$.

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Question 9

9. $\int \frac{x^2}{\left(2+3 x^3\right)^3} d x$.

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Question 10

10. $\int \frac{x d x}{\sqrt{x+4}}, x>0$.

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Question 11

11. $\int \frac{x^{m-1}}{\sqrt{1-x^m}} d x$.

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Question 12

12. $\int \frac{2 x^3}{4+x^8} d x$.

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Question 13

13. $\int \frac{x^3 d x}{\left(4-x^4\right)^2}$.

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Question 14

14. $\int x^{-1 / 2} \operatorname{cosec}^2 \sqrt{x} d x$.

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Question 15

15. $\int \cot x \log \sin x d x$.

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Question 16

16. $\int \frac{x}{e^{x^2}} d x$.

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Question 17

17. $\int \frac{x^2}{16+25 x^6} d x$.

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Question 18

18. $\int \frac{d x}{x^{1 / 2}+x^{1 / 3}}$

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Question 19

19. $\int x \cos ^3 x^2 \sin x^2 d x$.

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Question 20

20. $\int \frac{\left(e^{5 \log x}-e^{4 \log x}\right)}{\left(e^{3 \log x}-e^{2 \log x}\right)} d x$.

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Question 21

21. $\int e^x(1+x) \operatorname{cosec}^2\left(x e^x\right) d x$.

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Question 22

22. $\int \frac{\cos x d x}{\sqrt{4-\sin ^2 x}}$.

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Question 23

23. $\int \frac{x^4+1}{x^6+1} d x$.

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Question 24

24. $\int \frac{x^3 d x}{\sqrt{1-x^8}}$