Question

integrate -2to2 limit |1-x²|dx=?​

Answer 1

Answer:

$\displaystyle{\rightarrow \left(-\frac{4}{3}\right)}$

Step-by-step explanation:

Given :

$\displaystyle{\int\limits^2_{-2} {1-x^2} \,dx }\\\\\\\displaystyle{\rightarrow \int\limits^2_{-2} {1-x^2} \,dx }\\\\\\\displaystyle{\rightarrow \left|x-\frac{x^3}{3} \right|^{2}_{-2}}\\\\\\\displaystyle{\rightarrow \left(2-\frac{2^3}{3} \right)-\left(-2-\frac{-2^3}{3} \right)}\\\\\\\displaystyle{\rightarrow \left(2-\frac{8}{3} \right)-\left(-2+\frac{8}{3} \right)}\\\\\\\displaystyle{\rightarrow \left(-\frac{2}{3}-\frac{2}{3}\right)} \\\\\\\displaystyle{\rightarrow \left(-\frac{4}{3}\right)}$