Hey can anybody help me by giving a step to step guide on how to work out an area enclosed by a curve please?.
Find the area enclosed by the curve: Y=4x^2 (x^2-2x+1). The axis and the ordinates x=1 and x=2.
thanks
$\displaystyle A = \int_1^2 4x^2(x^2-2x+1) \, dx$
$\displaystyle A = \int_1^2 4x^4 - 8x^3 + 4x^2 \, dx$
the antiderivative of $\displaystyle k x^n$ is $\displaystyle \frac{k x^{n+1}}{n+1}$
$\displaystyle \left[\frac{4x^5}{5} - 2x^4 + \frac{4x^3}{3}\right]_1^2$
$\displaystyle \left(\frac{128}{5} - 32 + \frac{32}{3}\right) - \left(\frac{4}{5} - 2 + \frac{4}{3}\right)$
I leave you to finish the arithmetic