What is the integral from 1 to 3 of sqrt((2-x)^2) ?

The integral from 1 to 3 of sqrt((2-x)^2) is 1

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integral from 1 to 3 of sqrt((2-x)^2)

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

1

Solution steps

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

Apply exponent rule:

a^{2} = ∣ a ∣

= \int_{1}^{3} ∣ (2 - x) ∣ d x

Eliminate Absolutes

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

\int_{1}^{2} 2 - x d x = \frac{1}{2}

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

= \frac{1}{2} + \frac{1}{2}

Simplify

\frac{1}{2} + \frac{1}{2} : 1

= 1

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What is the integral from 1 to 3 of sqrt((2-x)^2) ?
The integral from 1 to 3 of sqrt((2-x)^2) is 1