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Find I=int0^pi ln(1+cosx)dx...

Find `I=int_0^pi ln(1+cosx)dx`

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If I_I=int_0^(pi//2)cos(sinx)dx ,I_2=int_0^(pi/2)sin(cosx)dx \ ,a n d \ I_3=int_0^(pi/2)cosx dx , then find the order in which the values I_1,I_2,I_3, exist.

Find int(x+sinx)/(1+cosx)dx.

int _(0)^(pi/2) log(cotx)dx

Evaluate: int_0^pi log(1+cosx)dx

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

int_(0)^((pi)/(2))log(sinx)dx=int_(0)^((pi)/(2))log(cosx)dx=(pi)/(2)log.(1)/(2)

Evaluate : int _(0)^(pi)(sin x+cosx)dx

Suppose M = int_0^(pi/2) cosx/(x+2) dx , N = int_0^(pi/4) sinxcosx/(x+1)^2 dx . Then the value of (M - N) equals

The value of (dI)/(da) when I=int_(0)^(pi//2) log((1+asinx)/(1-asinx)) (dx)/(sinx) (where |a|lt1 ) is

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Find the value of int(0)^(1){(sin^(-1)x)//x}dx.

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  2. Show that int0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive int...

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  3. Find I=int0^pi ln(1+cosx)dx

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  4. The value of inta^b(x-a)^3(b-x)^4dx is

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  5. The value of the integral int(-1//2)^(1//2) {((x+1)/(x-1))^(2)+((x-1...

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  6. The value of int(-a)^a(cos^(- 1)x-sin^(- 1)sqrt(1-x^2))dx is (a>0) w...

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  7. If f is an odd function, then evaluate I=int(-a)^a(f(sinx)dx)/(f(cosx...

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  8. Evaluate : int0^(pi/4)log(1+tanx)dx.

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  9. Evaluate: int(-pi/4)^(pi/4)(x^9-3x^5+7x^3-x+1)/(cos^2x)dx

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  10. Let a+b=4,w h e r ea<2,a n dl e tg(x) be a differentiable function. If...

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  11. Evaluate: int(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}...

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  12. If Un=int0^pi(1-cosnx)/(1-cosx)dx , where n is positive integer or zer...

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  13. Evaluate: int(-1)^1(x^3+|x|+1)/(x^2+2|x|+1)dx

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  14. Find the value of int(-1)^(3/2)|xsinpix|dx

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  15. Evaluate: int(-pi/2)^(pi/2)sin^2xcos^2x(sinx+cosx)dx

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  16. int(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer...

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  17. Evaluate: inta^b cos x dx

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  18. Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in R....

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  19. Evaluate: ("lim")(n to oo)((1^2+2^2+3^3++n^2)(1^3+2^3+3^3++n^3))/(1^6+...

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  20. ifint(dx)/(x^2(x^n+1)^(((n-1)/n))=-[f(x)]^(1/n)+c ,t h e nf(x)i s (1+...

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