What is the integral from 0 to sqrt(x of)ycos(x^2) ?

The integral from 0 to sqrt(x of)ycos(x^2) is (xcos(x^2))/2

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integral from 0 to sqrt(x of)ycos(x^2)

\int_{0}^{x} y cos (x^{2}) d y

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

Solution steps

\int_{0}^{x} y cos (x^{2}) d y

Take the constant out:

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

= cos (x^{2}) \cdot \int_{0}^{x} y d y

Apply the Power Rule

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

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

Compute the boundaries:

\frac{x}{2}

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

Simplify

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

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What is the integral from 0 to sqrt(x of)ycos(x^2) ?
The integral from 0 to sqrt(x of)ycos(x^2) is (xcos(x^2))/2