What is the integral from 6 to 8 of 4x+50e^{-0.2x} ?

The integral from 6 to 8 of 4x+50e^{-0.2x} is 80.82442…

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integral from 6 to 8 of 4x+50e^{-0.2x}

\int_{6}^{8} 4 x + 50 e^{- 0.2 x} d x

80.82442 \dots

Solution steps

\int_{6}^{8} 4 x + 50 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}^{8} 4 x d x + \int_{6}^{8} 50 e^{- 0.2 x} d x

\int_{6}^{8} 4 x d x = 56

\int_{6}^{8} 50 e^{- 0.2 x} d x = 24.82442 \dots

= 56 + 24.82442 \dots

Simplify

= 80.82442 \dots

What is the integral from 6 to 8 of 4x+50e^{-0.2x} ?
The integral from 6 to 8 of 4x+50e^{-0.2x} is 80.82442…