First slide

Introduction to integration

Question

$\int_{- π}^{π} | π - | x ‖ dx is equal to$

Easy

A

$\frac{π^{2}}{2}$
B

$\sqrt{2} π^{2}$
C

$2 π^{2}$
D

$π^{2}$

Solution

$2 \int_{0}^{π} |π - x| d x = 2 \int_{0}^{π} (π - x) d x = 2 {[π x - \frac{x^{2}}{2}]}_{0}^{π} = 2 (π^{2} - \frac{π^{2}}{2}) = 2 \cdot \frac{π^{2}}{2} = π^{2}$

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