What is the integral from 2 to 6 of (8t^3-6t^{-2}) ?

The integral from 2 to 6 of (8t^3-6t^{-2}) is 2558

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integral from 2 to 6 of (8t^3-6t^{-2})

\int_{2}^{6} (8 t^{3} - 6 t^{- 2}) d t

2558

Solution steps

\int_{2}^{6} 8 t^{3} - 6 t^{- 2} d t

6 t^{- 2} = \frac{6}{t ^{2}}

= \int_{2}^{6} 8 t^{3} - \frac{6}{t ^{2}} 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_{2}^{6} 8 t^{3} d t - \int_{2}^{6} \frac{6}{t ^{2}} d t

\int_{2}^{6} 8 t^{3} d t = 2560

\int_{2}^{6} \frac{6}{t ^{2}} d t = 2

= 2560 - 2

Simplify

= 2558

\int_{- 1}^{0} (x^{5}) x^{3} + 1 d x

\int_{0}^{1} \frac{x ^{3}}{2} d x

\int_{- 4}^{2} \frac{1}{16 - x ^{2}} d x

\int_{- 1}^{1} - x^{2} d x

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

What is the integral from 2 to 6 of (8t^3-6t^{-2}) ?
The integral from 2 to 6 of (8t^3-6t^{-2}) is 2558