What is the integral from 3 to 8 of (x^3-pix^2) ?

The integral from 3 to 8 of (x^3-pix^2) is 4015/4-(485pi)/3

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integral from 3 to 8 of (x^3-pix^2)

\int_{3}^{8} (x^{3} - π x^{2}) d x

\frac{4015}{4} - \frac{485 π}{3}

Decimal

495.85918 \dots

Solution steps

\int_{3}^{8} 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_{3}^{8} x^{3} d x - \int_{3}^{8} π x^{2} d x

\int_{3}^{8} x^{3} d x = \frac{4015}{4}

\int_{3}^{8} π x^{2} d x = \frac{485 π}{3}

= \frac{4015}{4} - \frac{485 π}{3}

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What is the integral from 3 to 8 of (x^3-pix^2) ?
The integral from 3 to 8 of (x^3-pix^2) is 4015/4-(485pi)/3