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int0^pi(xtanx)/(secx+cosx)dxi s (pi^2)/...

`int_0^pi(xtanx)/(secx+cosx)dxi s` `(pi^2)/4` (b) `(pi^2)/2` (c) `(3pi^2)/2` (d) `(pi^2)/3`

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Given,
`I=int_0^(pi) (x tan x)/(sec x + cos x) dx `
`I=int_0^(pi) (x (sinx)/(cosx))/(1/(cosx) + cos x) dx `
`I=int_0^(pi) (x sinx)/(1 + cos^2 x) dx ->(1)`
`I=int_0^(pi) ((pi-x) sin(pi-x))/(1 + cos^2(pi-x)) dx` ...
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int_0^pi (xtanx)/(secx+tanx)dx

int_(0)^( pi)(x tan x)/(sec x+cos x)dx is (pi^(2))/(4)(b)(pi^(2))/(2)(c)(3 pi^(2))/(2) (d) (pi^(2))/(3)

int_(0)^(pi)(x tanx)/((secx+cosx))dx=(pi^(2))/(4)

The value of the integral int_0^oox/((1+x)(1+x^2))dx is (pi^)/2 (b) (pi^)/4 (c) (pi^)/6 (d) pi/3

int_0^21/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/2 (d) pi

int_(0)^(pi//2)(cosx)/((sinx+cosx))dx=(pi)/(4)

The value of the integral int_(pi//2)^(pi//2)(x^2ln(pi+x)/(pi-x))cosx\ dx is a. 0 b. (pi^2)/2-4 c. (pi^2)/2+4 d. (pi^2)/2

Prove that int_(0)^(pi)(xtanx)/((secx+tanx))dx=pi((pi)/(2)-1) .

int_0^(pi/2) (3+4cosx)/(4+3cosx)^2dx= (A) 3/4 (B) 1/2 (C) pi/4 (D) 1/4

int_0^(pi//2)(sinx)/(s in x+cos x)dx equals to pi//2 b. pi//4 c. pi//3 d. pi

RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. int0^1sqrt((1-x)/(1+x))dx= (pi)/2 (b) (pi)/2-1 (c) (pi)/2+1 (d) ...

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  2. int0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx equals (a)log(2/3) (b) l...

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  3. int0^pi(xtanx)/(secx+cosx)dxi s (pi^2)/4 (b) (pi^2)/2 (c) (3pi^2)/2...

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  4. int0^2 1/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/2 ...

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  5. int(-pi//2)^(pi//2)"sin"|x|dx is equal to 1 (b) 2 (c) -1 (d) ...

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  6. The value of the integral int0^oox/((1+x)(1+x^2))dx is (pi)/2 (b) ...

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  7. int0^3(3x+1)/(x^2+9)dx = (pi)/(12)+log(2sqrt(2)) (b) (pi)/2+log(2sqr...

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

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

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

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

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

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

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

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

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

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

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

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

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

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