What is the integral from-v to v of cos(u/v) ?

The integral from-v to v of cos(u/v) is v*2sin(1)

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integral from-v to v of cos(u/v)

\int_{- v}^{v} cos (\frac{u}{v}) d u

v \cdot 2 sin (1)

Solution steps

\int_{- v}^{v} cos (\frac{u}{v}) d u

Apply u-substitution

= \int_{- 1}^{1} cos (w) v d w

Take the constant out:

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

= v \cdot \int_{- 1}^{1} cos (w) d w

Use the common integral:

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

= v [sin (w)]_{- 1}^{1}

Compute the boundaries:

2 sin (1)

= v \cdot 2 sin (1)

What is the integral from-v to v of cos(u/v) ?
The integral from-v to v of cos(u/v) is v*2sin(1)