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∫|x-1| dx limit is from 0 to 3.

∫|x-1| dx
limit is from 0 to 3.

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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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