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The value of the integral int (-pi//2)^...

The value of the integral ` int _(-pi//2)^(pi//2) sqrt(cos x - cos ^(3) x ) ` dx is

A

0

B

`4/3`

C

`2/3`

D

`1/5`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l =int_(-pi//2)^(pi//2)sqrt(cosx-cos^(3)x)dx`
`=int_(-pi//2)^(pi//2)sqrt(cosx)|sinx|dx`
`=2int_(0)^(pi//2)sqrt(cosx)sinxdx`
Put `cosx=trArr-sin xdx =dt`
`thereforel =-2int_(1)^(0)sqrt(t)dt=-(4)/(3)[t^(3//2)]_(1)^(0)=(4)/(3)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. If int (2)^(e) (1/(logx)-1/(logx)^(2))dx = a + b/(log2) , then

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  2. int (0)^(oo) (dx)/((x+ sqrt(x^(2)+1))^(3)) is equal to

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  3. The value of the integral int (-pi//2)^(pi//2) sqrt(cos x - cos ^(3) ...

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  4. The value of I=overset(0)underset(-2)int{x^(3)+3x^(2)+3x+3+(x+1)cos(...

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  5. int (alpha)^(beta) sqrt((x-alpha)/(beta -x)) dx is equal to

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  6. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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  7. The value overset(2)underset(-2)int {p" In"((1+x)/(1-x))+q" In "((1-...

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  8. Let F (x) = f(x) + f ((1)/(x)), where f (x) = int (1) ^(x ) (log t)/(1...

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  9. If 2f(x) - 3 f(1//x) = x," then " int(1)^(2) f(x) dx is equal to

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  10. int (0)^(2pi) sin^(6) x cos^(5) x dx is equal to

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  11. int (-3pi//2)^(-pi//2) [ ( x + pi)^(3) + cos^(2) x ] dx is equalt to

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  12. int (0)^(3) (3x+1)/(x^(2)+9) dx =

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  13. underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n) is

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  14. int (-1//2)^(1//2) cos x log ((1+x)/(1-x)) dx = k log 2 , then k equ...

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  15. The value of the integral int (0)^(pi//2) sin ^(5) x dx is

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  16. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

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  17. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

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  18. The value of int (0)^(pi//2) sin ^(8) x dx is

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  19. The value of overset(pi)underset(-pi)int(1-x^(2)) sin x cos^(2) x" dx"...

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  20. int (0)^(1) (xdx)/([x + sqrt(1-x^(2))]sqrt(1-x^(2))) is equal to

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