Find the area bounded by the curves `y=4-x^2` and the lines `y=0andy=3`

Explanation

We have ,
`y=4-x^{2}` can be written as `x^{2}=4-y`

This curve is symmetrical about y-axis and does not lie beyond y=4 when y>4, where ,`x^{2}` is negative and x becomes imaginary.

`therefore` the required area = area between the line `y=0` ( x-axis ) and `y=3` as shaded region
Area of A B C D`=int_{0}^{3} x d y=int_{0}^{3} sqrt{4-y} d y`

By integrating w.r.t y


`=[frac{(4-y)^{frac{3}{2}}}{frac{3}{2}(-1)}]_{1}^{3}=-frac{2}{3}[(4-y)^{frac{3}{2}}]_{0}^{3}`

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