What is the integral from-H to H of cos((ypi)/(2H)) ?

The integral from-H to H of cos((ypi)/(2H)) is (4H)/pi

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integral from-H to H of cos((ypi)/(2H))

\int_{- H}^{H} cos (\frac{y π}{2 H}) d y

\frac{4 H}{π}

Solution steps

\int_{- H}^{H} cos (\frac{y π}{2 H}) d y

Apply u-substitution

: \int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{2 H cos ( u )}{π} d u

= \int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{2 H cos ( u )}{π} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2 H}{π} \cdot \int_{- \frac{π}{2}}^{\frac{π}{2}} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{2 H}{π} [sin (u)]_{- \frac{π}{2}}^{\frac{π}{2}}

Compute the boundaries:

2

= \frac{2 H}{π} \cdot 2

Simplify

= \frac{4 H}{π}

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What is the integral from-H to H of cos((ypi)/(2H)) ?
The integral from-H to H of cos((ypi)/(2H)) is (4H)/pi