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

The integral from 1 to 3 of-1/(t^3)-3 is -58/9

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integral from 1 to 3 of-1/(t^3)-3

\int_{1}^{3} - \frac{1}{t ^{3}} - 3 d t

- \frac{58}{9}

Decimal

- 6.44444 \dots

Solution steps

\int_{1}^{3} - \frac{1}{t ^{3}} - 3 d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{1}^{3} \frac{1}{t ^{3}} d t = \frac{4}{9}

\int_{1}^{3} 3 d t = 6

= - \frac{4}{9} - 6

Simplify

- \frac{4}{9} - 6 : - \frac{58}{9}

= - \frac{58}{9}

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What is the integral from 1 to 3 of-1/(t^3)-3 ?
The integral from 1 to 3 of-1/(t^3)-3 is -58/9