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The correct evalution of int(0)^(pi//2) ...

The correct evalution of `int_(0)^(pi//2) sin x sin 2x dx ` is

A

`(4)/(3)`

B

`(1)/(3)`

C

`(3)/(4)`

D

`(2)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let ` l = int _(0)^(pi//2) sin x sin 2x dx = 2 int _(0)^(pi//2) sin^(2) x cos x dx `
Put ` t = sin x rArr dt = cos x dx `
` :. L = 2 int _(0)^(1) t^(2) dt = 2/3 [ t^(3) ] _(0)^(1) = 2/3 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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  3. int (0)^(pi //2)((root(n)(secx))/(root(n)(secx)+root(n)("cosec"x)))dx=

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  7. int(pi//2)^(pi//2)(cosx)/(1+e^(x))dx is equal to

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  8. int(0)^(pi//2)(1)/((1+tanx))dx=?

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  9. If int(0)^(1) tan^(-1) x dx = p , then the value of int(0)^(1) tan^(-1...

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  11. Which of the following is true ?

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  12. int(0)^(5) 1/((x-1)(x-2))dx is equal to

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  13. int(pi/4)^(pi/2) e^x(logsinx+cotx)dx

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  14. The value of int(0)^(pi) x sin^(3) x dx is

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  15. The value of int0 ^(pi/2) (cos3x+1)/(cosx - 1) dx is equal to

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  16. The value of underset(0)overset(1)int tan^(-1) ((2x-1)/(1+x-x^(2)))dx ...

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  17. If f is a continous function, then

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  18. The value of int(-pi)^(pi) sin^(3) x cos^(2) x dx is equal to

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  19. The value of int(-1)^(1) log ((x-1)/(x+1))dx is

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  20. int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)

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  21. int (1)^(2)e^(x) (1/x - 1/(x^(2)))dx is qual to

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