Question

Find the area of ​​the boundary by y = 2x² and y = x




Please urgent ....​

Answer 1

Question :

Find the area of the boundary by y = 2x² and y = x.

Concept :

The area bounded between two regions is a application of definite integration.

Solution :

Lets find the point of intersection of two curves.

$\tt 2{x}^{2} - x = 0$

$\tt \implies$ x(2x - 1) = 0

$\tt \implies$ x= 0 or x = $\frac{1}{2}$

$\tt \implies Area = \displaystyle \int \limits_{0}^{\frac{1}{2}} 2{x}^{2} - x \:dx$

$\tt \implies Area = 2\frac{{x}^{3}}{3} - \frac{{x}^{2}}{2}$

$\tt \implies Area = 2\frac{{1/2}^{3}}{3} - \frac{{1/2}^{2}}{2}$

$\tt \implies Area = 2\frac{1}{24} - \frac{1}{8}$

$\tt \implies Area = \frac{1}{12} - \frac{1}{8}$

$\tt \implies Area = \frac{2-3}{24}$

$\tt \implies Area = \frac{1}{24} \:sq.units$

Answer 2

Answer:

Sry I am very poor in mathematics