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

The integral from 3 to 4 of x^3-pix^2 is 175/4-(37pi)/3

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integral from 3 to 4 of x^3-pix^2

\int_{3}^{4} x^{3} - π x^{2} d x

\frac{175}{4} - \frac{37 π}{3}

Decimal

5.00369 \dots

Solution steps

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

\int_{3}^{4} x^{3} d x = \frac{175}{4}

\int_{3}^{4} π x^{2} d x = \frac{37 π}{3}

= \frac{175}{4} - \frac{37 π}{3}

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

\int_{0}^{1} (4 x + 7) d x

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

\int_{0}^{\infty} 6 x e^{6 x} d x

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

What is the integral from 3 to 4 of x^3-pix^2 ?
The integral from 3 to 4 of x^3-pix^2 is 175/4-(37pi)/3