What is the integral from 0 to 1 of ycos(x) ?

The integral from 0 to 1 of ycos(x) is cos(x) 1/2

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integral from 0 to 1 of ycos(x)

\int_{0}^{1} y cos (x) d y

cos (x) \frac{1}{2}

Solution steps

\int_{0}^{1} y cos (x) d y

Take the constant out:

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

= cos (x) \cdot \int_{0}^{1} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{0}^{1}

= cos (x) [\frac{y ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= cos (x) \frac{1}{2}

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What is the integral from 0 to 1 of ycos(x) ?
The integral from 0 to 1 of ycos(x) is cos(x) 1/2