_(-2)^1, x^2-1, dx equals: Option 1: 17/3 Option 2: 8/3 Option 3: 16/3 Option 4: 2/3

Answer: 8/3. Solution: x^2-1≥0 on [-2,-1] and ≤0 on [-1,1]. So the integral =_(-2)^(-1)(x^2-1)dx+_(-1)^1(1-x^2)dx=43+43=83.

Calculus

Integrals

Medium

applied

$\int_{-2}^{1}|x^2-1|dx$ equals:

$17/3$

$8/3$

$16/3$

$2/3$

✅ Correct Option: 2

$x^2-1\ge0$ on $[-2,-1]$ and $\le0$ on $[-1,1]$ . So the integral $=\int_{-2}^{-1}(x^2-1)dx+\int_{-1}^{1}(1-x^2)dx=\frac43+\frac43=\frac83$ .

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