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Find the area lying in the first quadran...

Find the area lying in the first quadrant and bounded by the curve `y=x^3` and the line `y=4xdot`

Text Solution

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The correct Answer is:
4 sq. units
`"The line "y=4x" meets "y=x^(3)" at "4x=x^(3)`.
`therefore" "x=0, 2,-2rArry=0,8,-8`
`rArr" "A=int_(0)^(2)(4x-x^(3))=(2x^(2)-(x^(4))/(4))_(0)^(2)=4` sq. units
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Knowledge Check

  • Area lying in the first quadrant and bounded by the curve y = x^(3) and the line y = 4x is

    A
    2
    B
    3
    C
    4
    D
    5

  • The area lying in the first quadrant and bounded by the circle x^2 + y^2 = 4 and the line x = sqrt 3y is :

    A
    `pi/3`
    B
    `pi/2`
    C
    `pi`
    D
    `pi/5`

  • Area lying in the first quadrant and bounded by the circle x^(2) +y ^(2) =4 and the lines x=0 and x=2 is :

    A
    `pi`
    B
    `pi/2`
    C
    `pi/2`
    D
    `pi/4`

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