Evaluate the integral ∫ |x|dx limit from -1 to 1?

1 Answer
Theodossis Papadopoulos
May 14, 2018

#int_-1^1|x|dx = 1#

Explanation:

You define the# f(x)=|x|#, which is same as defining
#f(x)=-x, x<0# and #f(x)=x, x>=0# at the same time
So you integral is #int_-1^1f(x)dx = int_-1^0-xdx + int_0^1xdx#
#=[-x^2/2]_-1^0 + [x^2/2]_0^1 = 0-(-1/2) + 1/2 - 0 = 1#

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