What is the integral from-5 to 5 of (-0.4x^2+10) ?

The integral from-5 to 5 of (-0.4x^2+10) is 66.66666…

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integral from-5 to 5 of (-0.4x^2+10)

\int_{- 5}^{5} (- 0.4 x^{2} + 10) d x

66.66666 \dots

Solution steps

\int_{- 5}^{5} - 0.4 x^{2} + 10 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_{- 5}^{5} 0.4 x^{2} d x + \int_{- 5}^{5} 10 d x

\int_{- 5}^{5} 0.4 x^{2} d x = 33.33333 \dots

\int_{- 5}^{5} 10 d x = 100

= - 33.33333 \dots + 100

Simplify

= 66.66666 \dots

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What is the integral from-5 to 5 of (-0.4x^2+10) ?
The integral from-5 to 5 of (-0.4x^2+10) is 66.66666…