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

The integral from 3 to 5 of (2x-5)^4 is 1562/5

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

\int_{3}^{5} (2 x - 5)^{4} d x

\frac{1562}{5}

Decimal

312.4

Solution steps

\int_{3}^{5} (2 x - 5)^{4} d x

Apply u-substitution

: \int_{1}^{5} \frac{u ^{4}}{2} d u

= \int_{1}^{5} \frac{u ^{4}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{5} u^{4} d u

Apply the Power Rule

: [\frac{u ^{5}}{5}]_{1}^{5}

= \frac{1}{2} [\frac{u ^{5}}{5}]_{1}^{5}

Compute the boundaries:

\frac{3124}{5}

= \frac{1}{2} \cdot \frac{3124}{5}

Simplify

= \frac{1562}{5}

\int_{- 2}^{2} x^{2} + 2 d x

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What is the integral from 3 to 5 of (2x-5)^4 ?
The integral from 3 to 5 of (2x-5)^4 is 1562/5