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

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