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

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

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Answer 1 · 2018-05-14T18:49:00

$\int_{- 1}^{1} | x | d x = 1$ $int_-1^1|x|dx = 1$

Explanation:

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

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

1 Answer

Explanation:

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