What is the integral from 1 to 2 of 1/((4-x)^3) ?

The integral from 1 to 2 of 1/((4-x)^3) is 5/72

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integral from 1 to 2 of 1/((4-x)^3)

\int_{1}^{2} \frac{1}{( 4 - x ) ^{3}} d x

\frac{5}{72}

Decimal Notation

0.06944 \dots

Solution steps

\int_{1}^{2} \frac{1}{( 4 - x ) ^{3}} d x

Apply u-substitution

: \int_{3}^{2} - \frac{1}{u ^{3}} d u

= \int_{3}^{2} - \frac{1}{u ^{3}} d u

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

= - \int_{2}^{3} - \frac{1}{u ^{3}} d u

Take the constant out:

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

= - (- \int_{2}^{3} \frac{1}{u ^{3}} d u)

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{2}^{3}

= - (- [- \frac{1}{2 u ^{2}}]_{2}^{3})

Simplify

= [- \frac{1}{2 u ^{2}}]_{2}^{3}

Compute the boundaries:

\frac{5}{72}

= \frac{5}{72}

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What is the integral from 1 to 2 of 1/((4-x)^3) ?
The integral from 1 to 2 of 1/((4-x)^3) is 5/72