What is the integral from 0 to 2 of 1/2 y^2 ?

The integral from 0 to 2 of 1/2 y^2 is 4/3

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integral from 0 to 2 of 1/2 y^2

\int_{0}^{2} \frac{1}{2} y^{2} d y

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

\int_{0}^{2} \frac{1}{2} y^{2} d y

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{2} y^{2} d y

Apply the Power Rule

= \frac{1}{2} [\frac{y ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= \frac{1}{2} \cdot \frac{8}{3}

Simplify

= \frac{4}{3}

\int - 4 e^{- 2 x} d x

\int_{0}^{1} 3 x^{2} + 1 d x

d er i v a t i v e \frac{10 x}{- 3 y ^{2}}

\frac{d}{d x} (- 4 x - 3)

x y^{^{'}} + 2 y = 2 x^{2} - 3 x

What is the integral from 0 to 2 of 1/2 y^2 ?
The integral from 0 to 2 of 1/2 y^2 is 4/3