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Evaluate :int0^(pi/2)(asinx+bcosx)/(sin(...

Evaluate :`int_0^(pi/2)(asinx+bcosx)/(sin(pi/4+x))dx`

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The correct Answer is:
`(pi (a+b))/(2 sqrt2)`
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MOTION-DEFINITE INTEGRATION -EXERCISE -3
  1. int (-1) ^(2) (x ^(2) -x)/(sqrt(x ^(2) + 4))

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  2. int (0) ^(pi//4) (xdx )/(cos x (cos x + sin x ))

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  3. Evaluate :int0^(pi/2)(asinx+bcosx)/(sin(pi/4+x))dx

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  4. int (0) ^(pi) ((ax +b) sec c tan x)/(4 + tan ^(2) x ) dx (a,b gt 0)

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  5. int0^pi((2x+3)sinx)/((1+cos^2x)dx

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  6. intxsin^(- 1)[1/2sqrt((2a-x)/a)]dx

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  7. f,g, h , are continuous in [0, a],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-...

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  8. Evaluate int0^1(dx)/((5+2x-2x^2)(1+e^(2-4x))) dx

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  9. The value of the integral underset(0)overset(pi)int (xdx)/(1+cos alpha...

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  10. int (0) ^(pi//4) (x ^(2) (sin 2x -cos 2x ))/((1+ sin 2x ) cos ^(2) x) ...

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  11. Evaluate: int ( 0 ) ^(pi) e ^(|cos x|)( 2 sin ((1)/(2)cos x )+ 3 cos...

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  12. It is known that f(x) is an odd function in the interval [p/2, p/2] an...

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  13. The value of int(-1)^2{2x}dx is (where function () denotes fractional ...

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  14. If y=x^(int1^x ln t dt), find (dy)/(dx) at x=e.

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  15. Evaluate (lim)(n->oo)n^2int(-1//n)^(1//n)(2010 s in x+2012cosx)|x|d...

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  16. Prove the following inequalty sqrt3/8<int(pi/4)^(pi/3)sinx/x dx<sqrt2/...

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  17. Prove that 4le int(1)^(3) sqrt(3+x^(3)) dx le 2sqrt30.

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  18. Prove that pi/6<int0^1(dx)/(sqrt(4-x^2-x^3))<pi/(4sqrt(2))

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  19. prove it 2e^(-1/4) < int0^2e^(x^2-x)dx < 2e^2

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  20. If a lt overset(2pi)underset(0)int (1)/(10+3 cos x)dx lt b. Then the o...

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