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Evaluate the following integral: int0^(p...

Evaluate the following integral: `int_0^(pi//2)(cos x)/(1+sin^2x)dx`

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Given:`int_0^(pi/2)(cosx)/(1+sin^2x)dx`
Let `sinx=t implies cosx dx=dt`
`I=int_0^1 1/(1+t^2)dt`
`I=[tan^(-1)t]_0^1`
`I=tan^(-1)(1)-tan^(-1)(0)`
`I=tan^(-1)(tan(pi/4))-tan^(-1)(tan(0))`
`I=pi/4`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integral: int0^1(1-x)/(1+x)dx

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  2. Evaluate the following integral: int0^(pi//2)(sin^2x)/((1+cos x)^2)dx

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  3. Evaluate the following integral: int0^(pi//2)(cos x)/(1+sin^2x)dx

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  4. Evaluate the following integrals: int0^1sqrt((1-x)/(1+x))dx

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  5. Evaluate the following integral: int0^(pi//4)cos^4xsin^3x\ dx

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  6. Evaluate the following integral: int0^(pi//2)x^2cos2x\ dx

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  7. Evaluate the following integral: int2^4(x^2+x)/(sqrt(2x+1))dx

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  8. int0^1(cos^(- 1)x)^2dx

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  9. Evaluate the following integral: int1^2x\ sqrt(3x-2)\ dx

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  10. Evaluate the following integral: int0^1cos^(-1)x\ dx

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  11. Evaluate the following integral: int0^1cos^(-1)((1-x^2)/(1+x^2))dx

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  12. Evaluate the following integral: int0^(1//sqrt(3))tan^(-1)((3x-x^3)/(1...

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  13. If int0^(pi/3)(cosx)/(3+4sinx) dx=k log((3+2sqrt(3))/3), then k is equ...

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  14. Evaluate the following integral: int0^(pi//2)(sinx)/(sqrt(1+cosx))dx

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  15. int0^pisin^3x(1+2cosx)(1+cosx)^2dx

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  16. Evaluate the following integral: int0^(pi//4)sin2x sin\ 3x\ dx

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  17. Evaluate the following integral: int1^2 1/(x^2)e^(-1//x)dx

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  18. Evaluate the following integral: int0^1log(1+x)dx

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  19. Evaluate: int0^1x(tan^(-1)x)^2dx

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  20. Evaluate the following integral: int1^2(x+3)/(x(x+2))dx

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