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The value of the integral underset(0)ove...

The value of the integral `underset(0)overset(pi)int (xdx)/(1+cos alpha sinx), 0 lt alpha lt pi`, is

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The correct Answer is:
`I=[{:((pialpha)/(sin alpha )if alpha in (0, pi)), ((pi)/(sin alpha) (alpha - 2pi) if alpha in (pi"," 2pi)):}`
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MOTION-DEFINITE INTEGRATION -EXERCISE -3
  1. 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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  2. Evaluate int0^1(dx)/((5+2x-2x^2)(1+e^(2-4x))) dx

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Prove the inequalities 1/2 le int (0) ^(2) (dx)/(2+x ^(2)) le 5/6

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  16. Evaluate lim ( n to oo) sum( r =1) ^(n -1) (1)/(sqrt(n ^(2) -r ^(2))...

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  17. lim(n->oo) 3/n[1+sqrt(n/(n+3)) + sqrt(n/(n+6)) + sqrt(n/(n+9)) +.........

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  18. Evaluate lim ( n to oo) 1/n [ (1)/( n + 1)+ (2)/(n + 2)+...+ (3n )/(...

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  19. Evaluate: ("lim")(nvecoo)[(n !)/(n^n)]^(1//n)

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  20. Dupose g(x) is the inverse of f (x) and f (x) has a domain x in [a,b]....

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