What is the integral from 0 to y of 2xyz ?

The integral from 0 to y of 2xyz is xy^3

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integral from 0 to y of 2xyz

\int_{0}^{y} 2 x yz d z

x y^{3}

Solution steps

\int_{0}^{y} 2 x yz d z

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

= x y^{3}

\int_{0}^{1} e^{- i wt} d t

\int_{0}^{2} \frac{1}{( 2 - x ) ^{\frac{4}{5}}} d x

\int_{0}^{1} 1 + x^{2} x d x

\int_{0}^{2 x} sin (t^{2}) d t

\int_{- 5}^{0} 1 d x

What is the integral from 0 to y of 2xyz ?
The integral from 0 to y of 2xyz is xy^3