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

The value of the integral `int_(0)^(1)(dx)/(x^(2)+2xcosalpha+1)`, where `0 lt alpha lt (pi)/(2)`, is equal to :

A

`sin alpha`

B

`alpha sin alpha`

C

`(alpha)/(2sin alpha)`

D

`(alpha)/(2) sin alpha`

Text Solution

Verified by Experts

The correct Answer is:
C
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1 Part-II
  1. If int(1)^(x) (dt)/(|t|sqrt(t^(2)-t)) = (pi)/(6), then x can be equal ...

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  2. The value of the integral int(0)^(1)(dx)/(x^(2)+2xcosalpha+1), where 0...

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  3. If f(x)={{:(x,xlt1),(x-1,xge1):}, then underset(0)overset(2)intx^(2)f(...

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  4. If f(0) = 1 , f(2) = 3, f'(2) = 5 and f'(0) is finite, then int(0)^(1...

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  5. int(0)^(pi)|1+2cosx| dx is equal to :

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  6. The value of int(1)^(3) (|x-2|+[x])dx is ([x] stands for greatest inte...

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  7. int(0)^(oo)[2e^(-x)] dx. Where [*] denotes the greatest integer funct...

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  8. int(lnpi-ln2)^(lnpi) (e^(-x))/(1-cos(2/3e^(x))) dx is equal to

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  9. If I(1)=int(n)^(e^(2))(dx)/(lnx) and I(2) = int(1)^(2)(e^(x))/(x) dx(1...

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  10. int(0)^(pi//4)(x.sinx)/(cos^(3)x) dx equal to :

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  11. The value if definite integral int(3/2)^(9/4)[sqrt(2x-sqrt(5(4x-5)))+s...

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  12. If int(ln2)^(x)(dx)/(sqrt(e^(x)-1))= (pi)/(6), then x is equal to

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  13. int(0)^(oo)(x^(2)+1)/(x^(4)+7x^(2)+1)dx=

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  14. Suppose for every integer n, .int(n)^(n+1) f(x)dx = n^(2). The value o...

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  15. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

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  16. int- 1^1cot^(- 1)((x+x^3)/(1+x^4))dx

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  17. int(2)^(0){x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)} dx is equal to

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  18. int(-1)^(1)xln(1+e^(x))dx=

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  19. If int(-1)^(3//2)|xsinpix|dx = (k)/(pi^(2)), then the value of k is :

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  20. The value of definite integral int0^(pi^2/4) dx/(1+sin^2 sqrtx+ cos^2 ...

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