What is the integral from 2 to 4 of 1/(|x-3|^{1/2)} ?

The integral from 2 to 4 of 1/(|x-3|^{1/2)} is 4

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integral from 2 to 4 of 1/(|x-3|^{1/2)}

\int_{2}^{4} \frac{1}{∣ x - 3 ∣ ^{\frac{1}{2}}} d x

4

Solution steps

\int_{2}^{4} \frac{1}{∣ x - 3 ∣ ^{\frac{1}{2}}} d x

Eliminate Absolutes

= \int_{2}^{3} \frac{1}{( - x + 3 ) ^{\frac{1}{2}}} d x + \int_{3}^{4} \frac{1}{( x - 3 ) ^{\frac{1}{2}}} d x

\int_{2}^{3} \frac{1}{( - x + 3 ) ^{\frac{1}{2}}} d x = 2

\int_{3}^{4} \frac{1}{( x - 3 ) ^{\frac{1}{2}}} d x = 2

= 2 + 2

Simplify

= 4

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What is the integral from 2 to 4 of 1/(|x-3|^{1/2)} ?
The integral from 2 to 4 of 1/(|x-3|^{1/2)} is 4