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

The integral from 0 to 1 of e^{-x}+3x^2 is -1/e+2

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

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

- \frac{1}{e} + 2

Decimal

1.63212 \dots

Solution steps

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

\int_{0}^{1} e^{- x} d x = 1 - \frac{1}{e}

\int_{0}^{1} 3 x^{2} d x = 1

= 1 - \frac{1}{e} + 1

Simplify

= - \frac{1}{e} + 2

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