What is the integral from 0 to 2x of (ye^{x^3}) ?

The integral from 0 to 2x of (ye^{x^3}) is e^{x^3}*2x^2

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integral from 0 to 2x of (ye^{x^3})

\int_{0}^{2 x} (y e^{x^{3}}) d y

e^{x^{3}} \cdot 2 x^{2}

Solution steps

\int_{0}^{2 x} y e^{x^{3}} d y

Take the constant out:

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

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

Apply the Power Rule

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

= e^{x^{3}} [\frac{y ^{2}}{2}]_{0}^{2 x}

Compute the boundaries:

2 x^{2}

= e^{x^{3}} \cdot 2 x^{2}

\int_{y}^{y^{3}} e^{\frac{x}{y}} d x

\int_{x}^{3} cos (t^{3}) d t

\int_{0}^{5} π x d x

\int_{0}^{2} (x^{2} e^{x^{3}}) d x

\int_{a}^{b} e^{t x} d x

What is the integral from 0 to 2x of (ye^{x^3}) ?
The integral from 0 to 2x of (ye^{x^3}) is e^{x^3}*2x^2