What is the integral from 0 to 1 of (e^x-x-5) ?

The integral from 0 to 1 of (e^x-x-5) is e-13/2

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integral from 0 to 1 of (e^x-x-5)

\int_{0}^{1} (e^{x} - x - 5) d x

e - \frac{13}{2}

Decimal Notation

- 3.78171 \dots

Solution steps

\int_{0}^{1} e^{x} - x - 5 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} x d x - \int_{0}^{1} 5 d x

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

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

\int_{0}^{1} 5 d x = 5

= e - 1 - \frac{1}{2} - 5

Simplify

e - 1 - \frac{1}{2} - 5 : e - \frac{13}{2}

= e - \frac{13}{2}

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What is the integral from 0 to 1 of (e^x-x-5) ?
The integral from 0 to 1 of (e^x-x-5) is e-13/2