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Ifx=intc^(sint)sin^(-1)z dz ,y=intk^(sqr...

`Ifx=int_c^(sint)sin^(-1)z dz ,y=int_k^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)/(dx) is \ equals `

A

`(tant)/(2t)`

B

`(tant)/(t^(2))`

C

`(tan t)/(2t^(2))`

D

`(tan t^(2))/(2t^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`(dx)/(dt)=sin^(-1)(sint)cost=tcost`
and `(dy)/(dt)=(sint)/(sqrt(t)) . 1/(2sqrt(t))= (sin t)/(2t)` or `(dy)/(dx)= (sint)/(2t . t cost)=(tant)/(2t^(2))`
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -SCQ_TYPE
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