Question #f7ed1

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Mar 13, 2017

#int_{-1}^{1} abs(x) dx = 1#

Explanation:

#f(x)# is a piecewise function.

#f(x) = {(x if x >= 0),(-x if x < 0) ]#

Hence, separate the integral into 2 parts.

#int_{-1}^{1} f(x) dx = int_{-1}^{0} f(x) dx + int_{0}^{1} f(x) dx#

#= int_{-1}^{0} (-x) dx + int_{0}^{1} x dx#

#= [-x^2/2]_{-1}^0 + [x^2/2]_0^1#

#= 1/2 + 1/2#

#= 1#

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