What is the integral from 4 to 5 of (x^3-pix^2) ?

The integral from 4 to 5 of (x^3-pix^2) is 369/4-(61pi)/3

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integral from 4 to 5 of (x^3-pix^2)

\int_{4}^{5} (x^{3} - π x^{2}) d x

\frac{369}{4} - \frac{61 π}{3}

Decimal

28.37094 \dots

Solution steps

\int_{4}^{5} x^{3} - π x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{4}^{5} x^{3} d x - \int_{4}^{5} π x^{2} d x

\int_{4}^{5} x^{3} d x = \frac{369}{4}

\int_{4}^{5} π x^{2} d x = \frac{61 π}{3}

= \frac{369}{4} - \frac{61 π}{3}

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What is the integral from 4 to 5 of (x^3-pix^2) ?
The integral from 4 to 5 of (x^3-pix^2) is 369/4-(61pi)/3