What is the integral from 0 to sqrt(y of)4x^2z^3 ?

The integral from 0 to sqrt(y of)4x^2z^3 is x^2y^2

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integral from 0 to sqrt(y of)4x^2z^3

\int_{0}^{y} 4 x^{2} z^{3} d z

x^{2} y^{2}

Solution steps

\int_{0}^{y} 4 x^{2} z^{3} d z

Take the constant out:

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

= 4 x^{2} \cdot \int_{0}^{y} z^{3} d z

Apply the Power Rule

: [\frac{z ^{4}}{4}]_{0}^{y}

= 4 x^{2} [\frac{z ^{4}}{4}]_{0}^{y}

Compute the boundaries:

\frac{y ^{2}}{4}

= 4 x^{2} \frac{y ^{2}}{4}

Simplify

= x^{2} y^{2}

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What is the integral from 0 to sqrt(y of)4x^2z^3 ?
The integral from 0 to sqrt(y of)4x^2z^3 is x^2y^2