What is the integral from 0 to 3 of-e^{-2y}+1 ?

The integral from 0 to 3 of-e^{-2y}+1 is -(e^6-1)/(2e^6)+3

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integral from 0 to 3 of-e^{-2y}+1

\int_{0}^{3} - e^{- 2 y} + 1 d y

- \frac{e ^{6} - 1}{2 e ^{6}} + 3

Decimal

2.50123 \dots

Solution steps

\int_{0}^{3} - e^{- 2 y} + 1 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{0}^{3} e^{- 2 y} d y + \int_{0}^{3} 1 d y

\int_{0}^{3} e^{- 2 y} d y = \frac{e ^{6} - 1}{2 e ^{6}}

\int_{0}^{3} 1 d y = 3

= - \frac{e ^{6} - 1}{2 e ^{6}} + 3

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What is the integral from 0 to 3 of-e^{-2y}+1 ?
The integral from 0 to 3 of-e^{-2y}+1 is -(e^6-1)/(2e^6)+3