What is the integral from 8 to 1 of 0.2x^2+1 ?

The integral from 8 to 1 of 0.2x^2+1 is -41.06666…

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integral from 8 to 1 of 0.2x^2+1

\int_{8}^{1} 0.2 x^{2} + 1 d x

- 41.06666 \dots

Solution steps

\int_{8}^{1} 0.2 x^{2} + 1 d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{8} 0.2 x^{2} + 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_{1}^{8} 0.2 x^{2} d x + \int_{1}^{8} 1 d x)

\int_{1}^{8} 0.2 x^{2} d x = 34.06666 \dots

\int_{1}^{8} 1 d x = 7

= - (34.06666 \dots + 7)

Simplify

= - 41.06666 \dots

\int_{2}^{5} 5^{2 x} d x

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\int_{6}^{12} \frac{36}{x} d x

\int_{- 1}^{2} (5 - 2 x) d x

\int_{0}^{1} 5 x + 7 d x

What is the integral from 8 to 1 of 0.2x^2+1 ?
The integral from 8 to 1 of 0.2x^2+1 is -41.06666…