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Find the continuous function f where (x^...

Find the continuous function `f` where `(x^4-4x^2)lt=f(x)lt=(2x^2-x^3)` such that the area bounded by `y=f(x),y=x^4-4x^2dot` then y-axis, and the line `x=t ,` where `(0lt=tlt=2)` is `k` times the area bounded by `y=f(x),y=2x^2-x^3`,y-axis , and line `x=t(w h e r e0lt=tlt=2)dot`

Text Solution

Verified by Experts

The correct Answer is:
`f(x)=1/(k+1)[x^4-kx^3+(2k-4)x^2]`
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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

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    2
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    `(9)/(4)`
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