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The value of the integral int(0)^(1)(dx)...

The value of the integral `int_(0)^(1)(dx)/(x^(2)+2x cos alpha +1),0ltalpha lt pi` is

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The correct Answer is:
`(alpha )/(2 sin alpha)if a ne 0 ; 1/2 if alpha =0`
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MOTION-DEFINITE INTEGRATION -ELEMENTRAY EXERCISE
  1. int (0) ^(1) x tan ^(-1) x dx =

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  2. Suppose that f,f^prime and f prime prime are continuous on [0, ln 2] a...

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  3. The value of the integral int(0)^(1)(dx)/(x^(2)+2x cos alpha +1),0ltal...

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  4. int (a) ^(b) (dx)/( sqrt(1 + x ^(2))) where a = (e-e^(-1))/( 2 ) &b = ...

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  5. int (x^(x)(x^(2x)+1)("ln"x+1))/(x^(4x)+1)dx

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  6. int (0) ^(1) x ^(5) sqrt((1 + x ^(2))/(sqrt(1- x^(2))))dx

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  7. Suppose that the function f, g, f',and g' are continuous over [0,1], g...

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  8. The value of the integral overset(pi//4)underset(0)int (sin theta+cos ...

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  9. int (0) ^(pi) sin ^(2) theta cos theta d theta

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  10. Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(...

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  11. int (0) ^(pi//2) (x + sin x )/(1 + cos x ) dx

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  12. Let A = int (3//4) ^(4//3) (2x ^(2) + x +1 )/( x ^(3) + x ^(2) + x + 1...

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  13. int (2 -x ^(2))/( ( a + 1) (1- x ^(2)))dx

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  14. int(-1)^1(d/dx(1/(1+e^(1/x))))dx

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  15. int (1) ^(e ) (dx )/(ln (x ^(x) e ^(x)))

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  16. int (0) ^(pi)[ cos ^(2) ((3pi)/(8) - (x )/(4)) - cos ^(2) ((11pi)/(8)+...

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  17. If f(pi) =2 and int0^pi (f(x) + f''(x)) sinx dx =5 then f(0) is equal ...

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  18. int (a) ^(b ) (| x |)/(x ) dx

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  19. If f(x)=e^(-x)+2e^(-2x)+3 e^(-3x)+.....+oo, then int(ln2)^(ln3) f(x)dx...

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  20. int (0) ^(pi//2) sqrt((sec x - tan x )/(sec x + tan x )) (cosec x )/(s...

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