Question

Find the area of the region enclosed by the curves y= x³ - 2x² and y = 2x² - 3x

Answer 1

Ans:-

The area between curves is the area between a curve f(x) and a curve g(x) on an interval [a, b]

$A=\intop^b_a \mid f(x)-g(x)\mid dx$

here $f(x)= x^3 - 2x^2$ and $g(x)= 2x^2 - 3x$

So applying the formula $\intop^3_0 \mid x^3-2x^2-(2x^2-3x)\mid dx$

$\to \intop^3_0 \mid x^3-4x^2+3x\mid dx$

$[\dfrac{x^4}{4}-\dfrac{4x^3}{3}+\dfrac{3x^2}{2}]^3_0$

$\dfrac{37}{12} cm^2$