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Mathematics Question on applications of integrals

The area of the region A=[(x,y):0≤y≤x∣x∣+1A = [(x, y): 0 \leq y \leq x|x|+1 and −1≤x≤1]-1 \leq x \leq 1] in s units is :

A

23\frac{2}{3}

B

13\frac{1}{3}

C

2

D

43\frac{4}{3}

Answer

2

Explanation

Solution

The graph is a follows
∫−10(−x2+1)dx+∫01(x2+1)dx=2\int^{0}_{-1} \left(-x^{2} +1\right)dx + \int^{1}_{0} \left(x^{2} +1\right)dx = 2