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Question: The area between the curves y = x<sup>3</sup> and y =<img src="https://cdn.pureessence.tech/canvas_2...

The area between the curves y = x3 and y =is

A

5/12

B

12/5

C

5/3

D

5/4

Answer

5/12

Explanation

Solution

Curves meet at x = 0 & x = 1

\ Req. area = ∫01(x−x3)dx=[23x3/2−x44]01\int _ { 0 } ^ { 1 } \left( \sqrt { x } - x ^ { 3 } \right) d x = \left[ \frac { 2 } { 3 } x ^ { 3 / 2 } - \frac { x ^ { 4 } } { 4 } \right] _ { 0 } ^ { 1 } = 512\frac { 5 } { 12 }