Solveeit Logo
Login

Question

Question: \(\int_{- 2}^{2}{|1 - x^{2}|dx}\) is equal to...

∫−22∣1−x2∣dx\int_{- 2}^{2}{|1 - x^{2}|dx} is equal to

A

2

B

4

C

6

D

8

Answer

4

Explanation

Solution

I=∫−22∣1−x2∣dx=∫−2−1∣1−x2∣dx+∫−11∣1−x2∣dx+∫12∣1−x2∣dxI = \int_{- 2}^{2}{|1 - x^{2}|dx = \int_{- 2}^{- 1}{|1 - x^{2}|dx}} + \int_{- 1}^{1}{|1 - x^{2}|dx} + \int_{1}^{2}{|1 - x^{2}|dx}⇒ I=−∫−2−1(1−x2)dx+∫−11(1−x2)dx−∫12(1−x2)dxI = - \int_{- 2}^{- 1}{(1 - x^{2})dx} + \int_{- 1}^{1}{(1 - x^{2})dx - \int_{1}^{2}{(1 - x^{2}})dx}

⇒ I=43+43+43=4I = \frac{4}{3} + \frac{4}{3} + \frac{4}{3} = 4.