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Evaluate:int0^(pi//2)(cosx)/(1+cosx+sinx...

Evaluate:`int_0^(pi//2)(cosx)/(1+cosx+sinx)dx`

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`I=``int_0^(pi//2)(cosx)/(1+cosx+sinx)dx`
`I=``int_0^(pi//2)(cos(pi/2-x))/(1+cos(pi/2-x)+sin(pi/2-x))dx`
`I=``int_0^(pi//2)(sinx)/(1+cosx+sinx)dx`
thus,
`2I=``int_0^(pi//2)(sinx+cosx)/(1+cosx+sinx)dx` ...
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. int0^3(3x+1)/(x^2+9)dx = (pi)/(12)+log(2sqrt(2)) (b) (pi)/2+log(2sqr...

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  2. I10=int0^(pi/2)x^(10)sinx dx then I10+90I8 is (A) 10(pi/2)^6 (B) 10(p...

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  3. Evaluate:int0^(pi//2)(cosx)/(1+cosx+sinx)dx

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  4. Evaluate: int0^(pi//2)1/(3+2cosx)dx

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  5. Evaluate: int(pi//4)^(pi//2)cos2xlogsinxdx

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  6. integrate int0^(2pi) e^x . sin (pi/4 + x/2) dx

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  7. Evaluate: int0^1(2x)/(5x^2+1)dx

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  8. Evaluate:(i) int0^(pi//6)(2+3x^2)dx

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  9. Evaluate: (i)int0^4 1/(x+sqrt(x))dx (ii) int0^1(2x)/(5x^2+1)dx

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  10. Evaluate the following definite integrals (1-58): int1^2 1/(sqrt((x...

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  11. If (x) is of the form f(x)=a+b x+c x^2, show that int0^1f(x)d...

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  12. Evaluate: int0^oo1/((x^2+a^2)(x^2+b^2))dxdot

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  13. Evaluate the following integrals: int0^(pi//6)cos^(-3)2thetasin2th...

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  14. Evaluate the following integrals: int0^((pi)^(2//3))sqrt(x)cos^2x^(...

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  15. Evaluate the following integrals: int0^1(24x^3)/((1+x^2)^4)dx

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

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  17. If In=int0^(pi//4)tan^("n")x dx , prove that In+I(n-2)=1/(n-1)dot

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  18. If In=int0^(pi//4)tan^n x dx , show that 1/(I2+I4),1/(I3+I5),1/(I4+...

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  19. Evaluate: int0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx

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

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