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

The integral from sqrt(x) to 2 of ycos(x^2) is cos(x^2)(2-x/2)

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

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

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

Solution steps

\int_{x}^{2} 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_{x}^{2} y d y

Apply the Power Rule

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

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

Compute the boundaries:

2 - \frac{x}{2}

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

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