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Question: \(\int_{- 1}^{1}{max\{ x,x^{3}\} dx}\)equals-...

∫−11max{x,x3}dx\int_{- 1}^{1}{max\{ x,x^{3}\} dx}equals-

A

2

B

1/4

C

3/4

D

3/2

Answer

1/4

Explanation

Solution

∫−11max⁡{x,x3}dx\int_{- 1}^{1}{\max\{ x,x^{3}\} dx}= ∫−10x3dx\int_{- 1}^{0}{x^{3}dx}+ ∫01xdx\int_{0}^{1}{xdx}

= −14\frac{- 1}{4}+ 12\frac{1}{2}= 14\frac{1}{4}