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The area of the region bounded by the cu...

The area of the region bounded by the curve `y = 2x - x^2` and the line `y = x` is

A

1/6

B

1/4

C

1/3

D

1/2

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D

`"Area, "A=overset(1)underset(-1)int(e-e^(x^(2)))dx=2e-overset(1)underset(-1)inte^(x^(2))dx`
`y=e^(x^(2))`
`therefore" "log_(e)y=x^(2)`
`therefore" "x=pmsqrt(log_(e)y)`
`therefore" Area, "A=2overset(e)underset(1)intsqrt(log_(e)y)dy`
`"Now put "log_(e)y=t.`
`therefore" "y=e^(t)`
`therefore" "dy=e^(t)dt`
`"So, area "A=2overset(1)underset(0)intsqrt(t)" "e^(t)dt`
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Knowledge Check

  • Area of the region bounded by the curve y^(2) = 4x , y -axis and the line y = 3 is

    A
    2
    B
    `(9)/(4)`
    C
    `(9)/(3)`
    D
    `(9)/(2)`

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