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Ifint(sinx)^1t^2f(t)dt=1=1-s inx ,w h e ...

`Ifint_(sinx)^1t^2f(t)dt=1=1-s inx ,w h e r ex in (0,pi/2),` then find the value of `f(1/(sqrt(3)))dot`

A

3

B

`sqrt(3)`

C

`1//3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(d)/(dx)int_(sinx)^(1)t^(2)f(t)dt=(d)/(dx)(1-sinx)`
`rArr[1^(2)f(1).(0)]-(sin^(2)x).f(sinx).cosx=-cosx`
`" [by Leibnitz's rule]"`
`rArr" "f(sinx)=(1)/(Sin^(2)x)`
`therefore" "f((1)/(sqrt3))=(sqrt3)^(2)=3" "["put sin x"=(1)/(sqrt3)]`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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  7. int (0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) thet...

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  8. The value of the integral int (-a)^(a) (xe^(x^(2)))/(1+x^(2)) dx is

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  9. int (-pi//2)^(pi//2) (dx)/(1+cosx) is equal to

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  10. The value of int (0)^(12a) (f(x))/(f(x)+f(12a-x))dx is

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  11. If kint(0)^(1)xf(3x)dx=int(0)^(3)tf(t)dt, then the value of k is

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  12. lim(nto oo)+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+...(1)/(sqrt(n^(2...

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  13. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

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  14. Evaluate: ("lim")(nvecoo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt...

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  15. If f(x) = tanx-tan ^(3) x + tan^(5) x - tan ^(7) x + ... infty for o...

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  16. The value of int(0)^((pi)/(8))cos^(3)4 theta d theta is equal to -

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  17. int (0)^(pi//3) (cos x + sin x)/(sqrt(1+sin 2x))dx is equal to

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

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  19. The value of int (1)^(2) (dx)/((x+1) sqrt((x^2)-1)) is

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  20. If f(x)=|(sin x+sin x 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,...

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