Question

The area bounded by the curves $y=x^2$ and line $y=x$

• A. $\sin 1$
• B. $1-\sin 1$
• C. $1+\sin 1$
• D. None of these

Answer 1

The correct option is D None of these

Given

Curve $y=x^2\cdots \left(1\right)$

Line $y=x\cdots \left(2\right)$

Put $\left(2\right)$ in $\left(1\right)$

$⟹x=x^2$

$⟹x=0,x=1$

The area is given as

$⟹{\int }_0^{1}x-x^{2}dx$

$⟹{\frac{x^2}{2}-\frac{x^3}{3}|}_0^{1}dx$

$⟹\frac{1}{2}-\frac{1}{3}$

$⟹\frac{1}{6}$