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Grade 12Integral Calculus

∫|x-1| dx
limit is from 0 to 3.

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int_{0}^{3}|x-1|dx$
$I = \int_{0}^{1}|x-1|dx+\int_{1}^{3}|x-1|dx$
$I = \int_{0}^{1}(1-x)dx+\int_{1}^{3}(x-1)dx$
$I = (x-\frac{x^2}{2})_{0}^{1}+\int_{1}^{3}(x-1)dx$
$I = \frac{1}{2}+(\frac{x^2}{2}-x)_{1}^{3}$
$I = \frac{1}{2}+[(\frac{9}{2}-3)-(-\frac{1}{2})]$
$I = \frac{1}{2}+2$
$I = \frac{5}{2}$

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