Area bounded by the curve `y=x^3`, the x-axis and the ordinates `x = 2`and `x = 1`is(A) `-9` (B) `(-15)/4` (C) `(15)/4` (D) `(17)/4`

Explanation

`\A =\int_{x=-2}^{x} y d x, y<0 \text { on }[-2,0) \& y>0 \text { on }(0,1]`


`A =\int_{-2}^{0}-y d x+\int_{0}^{1} y d x \ =\int_{-2}^{0}-x^{3} d x+\int_{0}^{1} x^{3} d x`

=`\frac{x^{4}}{4} -\frac{x^{4}}{4}|_{-2} ^{0}`


=`\frac{1}{4}-\frac{0}{4}-(\frac{0}{4}-\frac{16}{4})=\frac{1}{4}+\frac{16}{4}=17 / 4 u^{2}`