What is the integral from 0 to 30 of (10-x/3)^2 ?

The integral from 0 to 30 of (10-x/3)^2 is 1000

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integral from 0 to 30 of (10-x/3)^2

\int_{0}^{30} (10 - \frac{x}{3})^{2} d x

1000

Solution steps

\int_{0}^{30} (10 - \frac{x}{3})^{2} d x

Apply u-substitution

: \int_{10}^{0} - 3 u^{2} d u

= \int_{10}^{0} - 3 u^{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{10} - 3 u^{2} d u

Take the constant out:

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

= - (- 3 \cdot \int_{0}^{10} u^{2} d u)

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{0}^{10}

= - (- 3 [\frac{u ^{3}}{3}]_{0}^{10})

Simplify

= 3 [\frac{u ^{3}}{3}]_{0}^{10}

Compute the boundaries:

\frac{1000}{3}

= 3 \cdot \frac{1000}{3}

Simplify

= 1000

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What is the integral from 0 to 30 of (10-x/3)^2 ?
The integral from 0 to 30 of (10-x/3)^2 is 1000