Question

This is an integration question.

Answer 1

Answer:
`(1,1),\ (1)/(3)`

Explanation:

Given

Equation of the curves are
`y=x^2,\ y^2=x`

The intersection of the curve is

`\Rightarrow y^4-y=1\\\\\Rightarrow y(y^3-1)=0\\\\\Rightarrow y=0,1\\`

So, x coordinates are
`x=0,1`

points of intersection are
`(0,0),(1,1)`

So, the area bounded between the curves

`\Rightarrow I=\int_(0)^(1)\left ( √(x)-x^2\right )dx\\\\\Rightarrow I=\int_(0)^(1)√(x)dx-\int_(0)^(1)x^2dx\\\\\Rightarrow I=\left ( (2)/(3)x^{(3)/(2)} \right )_0^1-\left ( (1)/(3)x^3 \right )_0^1\\\\\Rightarrow I=(2)/(3)\left ( 1-0 \right )-(1)/(3)\left ( 1^3-0 \right )\\\\\Rightarrow I=(2)/(3)-(1)/(3)\\\\\Rightarrow I=(1)/(3)`

The area bounded by them is
`(1)/(3)`