Question

Area bounded by the curve y = x³, the x-axis and the ordinates x = −2 and x = 1 is ______.

Options

• −9

• `(-15)/4`

• `15/4`

• `17/4`

Answer 1

Area bounded by the curve y = x³, the x-axis and the ordinates x = −2 and x = 1 is `underline(17/4)`.

Explanation:

The required area is the shaded region, as shown in the graph.

∴ Required area `= |int_-2^0 x^3 dx| + int_0^1  x^3  dx`

`= |[x^4/4]|_-2^0 + [x^4/4]_0^1`

`= |(0 - 16/4)| + (1/4 - 0)`

`= 16/4 + 1/4`

`= 17/4` square units