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`int_0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx)) dx`

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Evaluate: int_(0)^((pi)/(2))(sqrt(cosx))/(sqrt(sinx)+sqrt(cosx))dx

int_(0)^((pi)/(2))(sqrt(sinx)dx)/(sqrt(sinx)+sqrtcosx)

Evaluate of each of the following integrals int_(pi//6)^(pi//3)(sqrt("sin"x))/(sqrt(sinx)+sqrt(cosx))"d"x

int_(0)^(pi)sqrt(1+sinx)dx

Prove that I =int_(0)^(pi//2)(sqrt(secx))/(sqrt("cosec"x)+sqrt(secx))dx =pi/4

If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] , (0 lt x lt pi/2) , then (dy)/(dx)=

int _0^(pi/2) (sin^2x)/(sinx+cosx)dx

Prove That : cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x epsilon(0,(pi)/4)

Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x in (0,pi/4)

The value of int_(0)^((pi)/(2)) (2^(sinx)dx)/(2^(sinx)+2^(cosx)) is equal to -

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Match the statements/expression given in Column I with the values give...

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  2. If I1=int0^pixf(sin^3x+cos^2x)dxa n d I2=int0^(pi/2)f(sin^3x+cos^2x)d...

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  3. int0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx)) dx

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  4. Find the value of int0^1 2x^3-3x^2-x+1 3dxdot

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  5. If int0^oox^(2n+1)dote^(-x^2)dx=360 , then the value of n is

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  6. Evaluate: int0^oo(dx)/(1+x^2)

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  7. If I1=int0^(pi/2)costhetaf(sintheta+cos^2theta)d(theta) and I2=int0^(...

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  8. If f(a+b-x)=f(x), then prove that inta^b xf(x)dx=(a+b)/2inta^bf...

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  9. Let I1=int(-2)^2(x^6+3x^5+7x^4)/(x^4+2)dx and I2=int(-3)^1(2(x+1)^2+1...

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  10. Find the value of int0^(pi/2)sin2xdx

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  11. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

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  12. The value of int0^(pi/2)cos^2xdx

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  13. prove that |sint| is non-differentiable at t=pi.

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  14. Find the value of int0^1x(1-x)dx

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  15. Let Sn=sum(k=0)^n n/(n^2+kn+k^2) and Tn=sum(k=0)^(n-1) n/(n^2+kn+k^2) ...

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  16. The value of the definite integral int(sqrt2-1)^(sqrt(2)+1)(x^4+x^2+2...

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  17. If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, the...

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  18. L e tJ=int(-5)^(-4)(3-x^2)tan(3-x^2)dx and K=int(-2)^(-1)(6-6x+x^2) t...

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  19. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

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  20. Show that ("lim")(n vec oo)(1/(n+1)+1/(n+2)++1/(6n))=log6

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