Question

The area enclosed between the graph of y = x³ and the lines x = 0, y = 1, y = 8 is ______.

Options

• `45/4`

• 14

• 7

• None of these

Answer 1

The area enclosed between the graph of y = x³ and the lines x = 0, y = 1, y = 8 is `bbunderline(45/4)`.

Explanation:

Given curve is y = x³ or x = y^l/3

Considering the areas with y-axis, we find that required area

`∫_1^8 y ^(1/3) dy = [y^(4/3)/(4/3)]_1^8 = 3/4 [8^(4/3) −1^(4/3)]`

= `3/4 × (16 − 1) + 3/4 × 15`

= `45/4` sq.units