What is the integral from 0 to 1 of sqrt(1+cos(pix)) ?

The integral from 0 to 1 of sqrt(1+cos(pix)) is (2sqrt(2))/pi

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integral from 0 to 1 of sqrt(1+cos(pix))

\int_{0}^{1} 1 + cos (π x) d x

\frac{2 2}{π}

Decimal

0.90031 \dots

Solution steps

\int_{0}^{1} 1 + cos (π x) d x

Compute the indefinite integral:

\int 1 + cos (π x) d x = \frac{2 2}{π} sin (\frac{π x}{2}) + C

Compute the boundaries:

\int_{0}^{1} 1 + cos (π x) d x = \frac{2 2}{π} - 0

= \frac{2 2}{π} - 0

Simplify

= \frac{2 2}{π}

What is the integral from 0 to 1 of sqrt(1+cos(pix)) ?
The integral from 0 to 1 of sqrt(1+cos(pix)) is (2sqrt(2))/pi