What is the integral from 0 to 4 of (5piy^4)/4 ?

The integral from 0 to 4 of (5piy^4)/4 is 256pi

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integral from 0 to 4 of (5piy^4)/4

\int_{0}^{4} \frac{5 π y ^{4}}{4} d y

256 π

Decimal Notation

804.24771 \dots

Solution steps

\int_{0}^{4} \frac{5 π y ^{4}}{4} d y

Take the constant out:

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

= \frac{5 π}{4} \cdot \int_{0}^{4} y^{4} d y

Apply the Power Rule

: [\frac{y ^{5}}{5}]_{0}^{4}

= \frac{5 π}{4} [\frac{y ^{5}}{5}]_{0}^{4}

Compute the boundaries:

\frac{1024}{5}

= \frac{5 π}{4} \cdot \frac{1024}{5}

Simplify

= 256 π

\frac{d y}{d x} + y cos (x) = 3 cos (x)

\int \frac{x cos ( x ^{2} )}{sin ( x ^{2} )} d x

y^{^{''}} + 26 y^{^{'}} + 6 y = 0

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

y^{^{''}} + 64 y^{^{'}} = 0

What is the integral from 0 to 4 of (5piy^4)/4 ?
The integral from 0 to 4 of (5piy^4)/4 is 256pi