What is the integral from 0 to 2x^2 of 3xy ?

The integral from 0 to 2x^2 of 3xy is 6x^5

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integral from 0 to 2x^2 of 3xy

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

6 x^{5}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

2 x^{4}

= 3 x \cdot 2 x^{4}

Simplify

= 6 x^{5}

\int_{- 1}^{2} x (x + 1) (x - 2) d x

\int_{0}^{3} (3 - x)^{\frac{- 1}{2}} d x

\int_{- 6}^{1} x^{3} d x

\int_{1}^{2} (e^{3 t} - \frac{4}{t}) d t

\int_{0}^{1} e^{x} - e^{7 x - 6} d x

What is the integral from 0 to 2x^2 of 3xy ?
The integral from 0 to 2x^2 of 3xy is 6x^5