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Show that: int0^(pi//2)f(sin2x)sinxdx...

Show that: `int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot`

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If the function f : [-1,1] to R is continuous and even, then show that int_(0)^(pi//2)f(cos2x)cosxdx=sqrt(2)int_(0)^(pi//4)f(sin2x)cosxdx .

int_0^(pi/2) sqrt(cosx)sinxdx

Evaluate : int_0^(pi/2)x^2sinxdx

If I_1=int_0^(pi/2)f(sinx)sinxdx and I_2=int_0^(pi/2)f(cosx)cosxdx then I_1/I_2

Prove that : int_0^(pi/2)sqrt(1-sin2x)dx=2(sqrt(2)-1)

Show that (i) int_(0)^(pi//2)f(sinx) d x=int_(0)^(pi//2)f(cos x) d x (ii) int_(0)^(pi//2)f(tan x) d x=int_(0)^(pi//2)f(cot x) d x (iii) int_(0)^(pi//2)f(sin 2 x) sin xd x = int_(o)^(pi//2)f(sin 2x).cosx d x

Evaluate: int_0^(pi//4)sqrt(1+sin2x)dx (ii) int_0^(pi//4)sqrt(1-sin2x)dx

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

Evaluate : int_0^(pi/2)(sin^2x)/(sin x+cos x)dx

RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. Evaluate the following integrals: (1-35) int(-2)^2(3x^3+2|x|+1)/(x^...

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  2. Evaluate the following integrals: (1-35) int0^pixsinx cos^2x dx

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  3. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

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  4. For x >0,l e tf(x)=int1^x((log)e t)/(1+t)dtdot Find the function...

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  5. Evaluate the following integrals: (1-35) int0^(pi//2)(sin^n x)/(sin...

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  6. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx= pi^2

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  7. Prove that: int0^(pi//2)log|tanx+cotx|dx=pi(log)e2

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  8. Evaluate: int(-2)^2|xcospix|dx

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  9. Evaluate: int(-pi//2)^(pi//2)log(sinx+cosx)dx

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  10. Evaluate: int0^pixlogsinxdx

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  11. If int0^pi 1/(a+bcosx)dx=pi/sqrt(a^2-b^2), then int0^pi 1/(a+bcosx)^2d...

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  12. int0^1sqrt((1-x)/(1+x))dx= (a) (pi)/2 (b) (pi)/2-1 (c) (pi)/2+1 (d...

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

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

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  15. int0^21/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/...

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

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

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

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

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  20. The derivative of f(x)=int(x^2)^(x^3)1/((log)e t)dt ,(x >0), is 1/(...

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