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Let I=int0^1 (sinx)/sqrtx dx and J=int0^...

Let `I=int_0^1 (sinx)/sqrtx dx and J=int_0^1 (cos x)/sqrtx dx`. Then which of the following is true?

A

`I gt 2/3 and J lt 2`

B

`I gt 2/3 and J gt 2`

C

`I lt 2/3 and J lt 2`

D

`I lt 2/3 and J gt 2`

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Knowledge Check

  • Let I=int_(0)^(1) (sin x)/(sqrt(x))dx and I=int_(0)^(1) (cos x)/(sqrt(x))int dx . Then, which one of the following is true?

    A
    `I gt (2)/(3)" and "J gt 2`
    B
    `I lt (2)/(3)" and "J lt 2`
    C
    `I lt (2)/(3)" and "J gt 2`
    D
    `I gt (2)/(3)" and "J lt 2`

  • int cos sqrtx dx =…..

    A
    `2 [sqrtx sin sqrtx+cos sqrtx]+c`
    B
    `sqrtx sin sqrtx+1 cos sqrtx+c`
    C
    `2[sqrtx cos sqrtx + sin sqrtx]+c`
    D
    `(1)/(2) [sqrtx sin sqrtx-cos sqrtx]+c`

  • int(1-cossqrtx)/(sqrtx)dx=

    A
    `sqrtx-2sin sqrtx`
    B
    `2(sqrtx-sin sqrtx)+c`
    C
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    D
    `sqrtx+2sin sqrtx+c`

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