What is the integral from 0 to 2 of 4y^2 ?

The integral from 0 to 2 of 4y^2 is 32/3

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integral from 0 to 2 of 4y^2

\int_{0}^{2} 4 y^{2} d y

\frac{32}{3}

Decimal Notation

10.66666 \dots

Solution steps

\int_{0}^{2} 4 y^{2} d y

Take the constant out:

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

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

Apply the Power Rule

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

= 4 [\frac{y ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= 4 \cdot \frac{8}{3}

Simplify

= \frac{32}{3}

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\int_{- 1}^{1} x^{3} (x^{2} + 3)^{10} d x

\int_{0}^{\frac{π}{2}} \frac{sin ^{5} ( θ )}{4} d θ

\int_{0}^{3} \frac{x ^{3}}{3} d x

\int_{2}^{5} (2 + 3 x) d x

What is the integral from 0 to 2 of 4y^2 ?
The integral from 0 to 2 of 4y^2 is 32/3