What is the integral from 3 to 5 of pi(x-3)^3 ?

The integral from 3 to 5 of pi(x-3)^3 is pi4

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integral from 3 to 5 of pi(x-3)^3

\int_{3}^{5} π (x - 3)^{3} d x

π 4

Decimal

12.56637 \dots

Solution steps

\int_{3}^{5} π (x - 3)^{3} d x

Take the constant out:

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

= π \cdot \int_{3}^{5} (x - 3)^{3} d x

Apply u-substitution

: \int_{0}^{2} u^{3} d u

= π \cdot \int_{0}^{2} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{0}^{2}

= π [\frac{u ^{4}}{4}]_{0}^{2}

Compute the boundaries:

4

= π 4

\int_{- 3}^{4} 10 - 5 x d x

\int_{0}^{27} 10 3 x d x

\int_{3}^{4} 9 - x^{2} d x

\int_{0}^{\frac{π}{2}} (x sin (y)) d y

\int_{2}^{10} u (x) d x

What is the integral from 3 to 5 of pi(x-3)^3 ?
The integral from 3 to 5 of pi(x-3)^3 is pi4