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

The integral from 3 to x of-2/(t^3) is 1/(x^2)-1/9

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

\int_{3}^{x} - \frac{2}{t ^{3}} d t

\frac{1}{x ^{2}} - \frac{1}{9}

Solution steps

\int_{3}^{x} - \frac{2}{t ^{3}} d t

Take the constant out:

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

= - 2 \cdot \int_{3}^{x} \frac{1}{t ^{3}} d t

Apply the Power Rule

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

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

Compute the boundaries:

- \frac{1}{2 x ^{2}} + \frac{1}{18}

= - 2 (- \frac{1}{2 x ^{2}} + \frac{1}{18})

Simplify

= \frac{1}{x ^{2}} - \frac{1}{9}

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What is the integral from 3 to x of-2/(t^3) ?
The integral from 3 to x of-2/(t^3) is 1/(x^2)-1/9