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If f(x) rArr int(sin theta)^("cosec" th...

If f(x) `rArr int_(sin theta)^("cosec" theta) f(x)dx` equals

A

`sin theta+"cosec" theta`

B

`sin^(2)theta`

C

`"cosec" ^(2)theta`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`f((1)/(x))+x^(2)f(x)=0 rArr r(x)=-(1)/(x^(2))f((1)/(x))`
`:. l=underset(sin theta)overset("cosec "theta)int f(x)dxunderset(sin theta)overset("cosec "theta)int-(1)/(x^(2))f((1)/(x))dx=underset("cosec" theta)overset(sin theta)intf(t)dt" where " t=(1)/(x)`
`rArr I=-underset(sin theta)overset("cosec "theta)int f(t)dt=-I rArr 2I=0 rArr I=0`
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Section I - Solved Mcqs
  1. If n in N, then int(-n)^(n)(-1)^([x]) dx equals

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  2. The value of :.int(0)^([x]) (2^(x))/(2^([x]))dx is

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  3. If f(x) rArr int(sin theta)^("cosec" theta) f(x)dx equals

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  4. If f(x)={{:(e^(cosx), sin x, "for" |x|le2),(,2,"otherwise"):} then int...

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  5. The value of the integral int(e^(-1))^(e^(2)) |(log(e)x)/(x)|dx is

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  6. Let g(x)=int(0)^(x)f(t) dt, where f is such that (1)/(2)lef(t)le1 "fo...

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  7. Let f:(0, oo) in R and F(x) = int(0)^(x) f(t) dt. If F(x^(2))=x^(2)(1+...

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  8. The integral int( -1//2)^(1//2) {[x]+ in ((1+x)/(1-x))} dx equals

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  9. Let Tgt0 be a fixed real number. Suppose f is a cintinuous function s...

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  10. Let f(x)=int(1)^(x) sqrt(2-t^(2))dt. Then the real roots of the equati...

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  11. If f((1)/(x)) +x^(2)f(x) =0, x gt0 and I= int(1//x)^(x) f(t)dt, (1)/(...

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  12. If | int(a)^(b) f(x)dx|= int(a)^(b)|f(x)|dx,a ltb,"then " f(x)=0 has

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  13. Let f(x) be an odd continuous function which is periodic with period 2...

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  14. All the values of 'a' for which int(1)^(2) {a^(2)+(4-4a)x+4x^(3)}dxle1...

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  15. Let f (x) be a function defined by f(x)=int(0)^(x) t(t^(2)-3t+2)dt, 1 ...

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  16. If int(0)^(x){t}dt=int(0)^({x})t dt ("where" x gt0 neZ and and {*} rep...

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  17. Let f(x)=max. {x+|x|,x-[x]} , where [x] denotes the greatest integer l...

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  18. rArrint(0)^(oo) [(2)/(e^(x))]dx (where [*] denotes the greatest intege...

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  19. If rArr int(0)^(1) (e^(-t))/(t+1) dt =a, "then"int(b-1)^(b) (e^(-1))/(...

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  20. If rArr int(-1)^(-4) f(x)dx= 4 and int(2)^(-4) (3-f(x))dx=7 , then the...

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