What is the integral from 0 to 4 of 2sqrt(y) ?

The integral from 0 to 4 of 2sqrt(y) is 32/3

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integral from 0 to 4 of 2sqrt(y)

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

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{16}{3}

= 2 \cdot \frac{16}{3}

Simplify

= \frac{32}{3}

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

\int_{0}^{2} (2 x - 3) (4 x^{2} + 5) d x

\int_{0}^{9} (2 x)^{2} d x

\int_{1}^{e} \frac{1}{x ( 1 + x )} d x

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

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