The area bounded by the parabola y=x^2 and th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) To find the area bounded by the parabola $y=x^2$ and the line $y=x$,we first determine their points of intersection by setting $x^2 = x$.This give

Vedclass · Accepted Answer

$\frac{1}{6}$ sq. units

Vedclass · Answer

(D) To find the area bounded by the parabola $y=x^2$ and the line $y=x$,we first determine their points of intersection by setting $x^2 = x$.This gives $x^2 - x = 0$,which implies $x(x-1) = 0$.Thus,the points of intersection are $x=0$ and $x=1$.For $x \in [0, 1]$,the line $y=x$ lies above the parabola $y=x^2$.The required area $A$ is given by the integral:$A = \int_0^1 (x - x^2) dx$$A = \left[ \frac{x^2}{2} - \frac{x^3}{3} \right]_0^1$$A = \left( \frac{1^2}{2} - \frac{1^3}{3} \right) - (0 - 0)$$A = \frac{1}{2} - \frac{1}{3} = \frac{3-2}{6} = \frac{1}{6}$ sq. units.

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

Similar Questions

Reserpine is obtained from ...... .

Which of the following is the weakest base?

Rate constant varies with temperature by the equation $\log _{10} k =5-\frac{2000}{T}$. We can conclude that $\left( R =8.314\ J\ mol ^{-1} K^{-1}\right) :-$

Vedclass Test Series

Exam Paper Generator

Online Exam Module