What is the integral from 0 to 3 of (e^{x/3}-3) ?

The integral from 0 to 3 of (e^{x/3}-3) is 3e-12

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integral from 0 to 3 of (e^{x/3}-3)

\int_{0}^{3} (e^{\frac{x}{3}} - 3) d x

3 e - 12

Decimal

- 3.84515 \dots

Solution steps

\int_{0}^{3} e^{\frac{x}{3}} - 3 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}^{3} e^{\frac{x}{3}} d x - \int_{0}^{3} 3 d x

\int_{0}^{3} e^{\frac{x}{3}} d x = 3 (e - 1)

\int_{0}^{3} 3 d x = 9

= 3 (e - 1) - 9

Simplify

3 (e - 1) - 9 : 3 e - 12

= 3 e - 12

What is the integral from 0 to 3 of (e^{x/3}-3) ?
The integral from 0 to 3 of (e^{x/3}-3) is 3e-12