What is the integral from 2 to 3 of 5x^4-8x^3+1 ?

The integral from 2 to 3 of 5x^4-8x^3+1 is 82

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integral from 2 to 3 of 5x^4-8x^3+1

\int_{2}^{3} 5 x^{4} - 8 x^{3} + 1 d x

82

Solution steps

\int_{2}^{3} 5 x^{4} - 8 x^{3} + 1 d x

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}^{3} 5 x^{4} d x - \int_{2}^{3} 8 x^{3} d x + \int_{2}^{3} 1 d x

\int_{2}^{3} 5 x^{4} d x = 211

\int_{2}^{3} 8 x^{3} d x = 130

\int_{2}^{3} 1 d x = 1

= 211 - 130 + 1

Simplify

= 82

\int_{0}^{1} - 2 x + 3 d x

\int_{0}^{1} 4 - y^{2} d y

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

\int_{- a}^{a} (a^{2} - x^{2})^{2} d x

What is the integral from 2 to 3 of 5x^4-8x^3+1 ?
The integral from 2 to 3 of 5x^4-8x^3+1 is 82