What is the integral from 1 to 2 of (10x^4-9x^2) ?

The integral from 1 to 2 of (10x^4-9x^2) is 41

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integral from 1 to 2 of (10x^4-9x^2)

\int_{1}^{2} (10 x^{4} - 9 x^{2}) d x

41

Solution steps

\int_{1}^{2} 10 x^{4} - 9 x^{2} 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_{1}^{2} 10 x^{4} d x - \int_{1}^{2} 9 x^{2} d x

\int_{1}^{2} 10 x^{4} d x = 62

\int_{1}^{2} 9 x^{2} d x = 21

= 62 - 21

Simplify

= 41

What is the integral from 1 to 2 of (10x^4-9x^2) ?
The integral from 1 to 2 of (10x^4-9x^2) is 41