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intsqrt(1+sin((x)/(4)))dx is equal to...

`intsqrt(1+sin((x)/(4)))dx` is equal to

A

`B(sin.(x)/(8)-cos.(x)/(8))+c`

B

`(sin.(x)/(8)+cos.(x)/(8))+c`

C

`(1)/(8)(sin.(x)/(8)-cos.(x)/(8))+c`

D

`8(cos.(x)/(8)-sin.(x)/(8))+c`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that ,
`sqrt(1+sin2theta)=sintheta+costheta`
`intsqrt(1+sin.(x)/(4))dx`
`=int(sin.(x)/(8) +cos.(x)/(8))dx`
`=-8cos.(x)/(8)+8sin.(x)/(8)+c`
`=8(sin.(x)/(8)-cos.(x)/(8))+c`
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Knowledge Check

  • intsqrt(1+sin((x)/(2)))dx=

    A
    `4[sin((x)/(2))+cos((x)/(2))]+c`
    B
    `4[sin((x)/(4))-cos((x)/(4))]+c`
    C
    `sqrt(1-sin((x)/(2)))+c`
    D
    none of these

  • intsqrt((x)/(1-x^(3)))dx is equal to

    A
    `(2)/(3)sin^(-1)(x^(2//3))+C`
    B
    `(3)/(2)sin^(-1)(x^(2//3))+C`
    C
    `(3)/(2)sin^(-1)(x^(2//3))+C`
    D
    `(2)/(3)sin^(-1)(x^(2//3))+C`

  • intsqrt((x-1)/(x+1))dx is equal to

    A
    `2sqrt(x^(2)+1)+sin^(-1)x+C`
    B
    `sqrt(x^(2)-1)-sin^(-1)x+C`
    C
    `sqrt(x^(2)-1)+sin^(-1)x+C`
    D
    `(sqrt(x^(2)-1))/(2)+sin^(-1)x+C`

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