What is the integral from 6 to 11 of 4x-10xe^{-0.2x} ?

The integral from 6 to 11 of 4x-10xe^{-0.2x} is 92.98571…

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integral from 6 to 11 of 4x-10xe^{-0.2x}

\int_{6}^{11} 4 x - 10 x e^{- 0.2 x} d x

92.98571 \dots

Solution steps

\int_{6}^{11} 4 x - 10 x e^{- 0.2 x} 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_{6}^{11} 4 x d x - \int_{6}^{11} 10 x e^{- 0.2 x} d x

\int_{6}^{11} 4 x d x = 170

\int_{6}^{11} 10 x e^{- 0.2 x} d x = 77.01428 \dots

= 170 - 77.01428 \dots

Simplify

= 92.98571 \dots

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What is the integral from 6 to 11 of 4x-10xe^{-0.2x} ?
The integral from 6 to 11 of 4x-10xe^{-0.2x} is 92.98571…