Which of the following is larger?

Calculus Level 1

Which of the following is larger?

A . 1 2 x d x A.\large\int^{2}_{-1} |x| dx

B . 1 2 x d x B.\large\int^{2}_{-1} x dx

B B A A

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1 solution

Munem Shahriar
Nov 16, 2017

A = 1 2 x d x = 1 0 d x + 1 2 ( x ) d x = 1 2 + 2 5 2 \large A = \int^2_{-1} |x| dx = \int^0_{-1} dx + \int^2_{-1} (x) dx = \dfrac 12 +2 \implies \dfrac 52

B = 1 2 x d x = 2 1 2 3 2 \large B = \int^{2}_{-1} x dx = 2 - \dfrac 12 \implies \dfrac 32

Hence A > B A > B

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