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 Notation

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}

g (x) = \frac{5}{x ^{3}}

\frac{d}{d x} ((2 x + 1)^{5} (3 x - 2)^{7})

\frac{d}{d x} (e^{- 3 x} sin (π x - \frac{π}{8}))

\int \frac{x + 3}{x ^{2} - 4} d x

n = 1 \sum \infty 1 4^{n} x^{n} n!

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