The area (in square units) bounded by the curve `y=x^3`, the x-axis and the ordinates at `x = -2 and x= 1` is

Options

A. `-9`
B. `(-15)/(4)`
C. `(15)/(4)`
D. `(17)/(4)`

Answer

D

Explanation

Given curve is `y=x^(3)`
If we replace x by -x and y by -y then we get `y=x^(3)`.
Therefore, curve is symmetric in opposite quadrants and passes through the orgin (0, 0).

` :. ` Required area `=int_(-2)^(1)|x^(3)|dx`
`=int_(-2)^(0)|x^(3)|dx+int_(0)^(1)|x^(3)|dx`
`=int_(-2)^(0)(-x^(3))dx+int_(0)^(1)x^(3)dx`
`= -[(x^(4))/(4)]_(-2)^(0)+[(x^(4))/(4)]_(0)^(1)`
`= -[0-((-2)^(4))/(4)]+[(1)/(4)-0]`
`= -(-4)+((1)/(4))=(17)/(4)` sq. units.