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

The integral from-3 to 2 of e^{x+3} is e^5-1

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

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

e^{5} - 1

Decimal

147.41315 \dots

Solution steps

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

e^{x + 3} = e^{3} e^{x}

= \int_{- 3}^{2} e^{3} e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{3} \cdot \int_{- 3}^{2} e^{x} d x

Use the common integral:

\int e^{x} d x = e^{x}

= e^{3} [e^{x}]_{- 3}^{2}

Compute the boundaries:

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

= e^{3} (e^{2} - \frac{1}{e ^{3}})

Simplify

= e^{5} - 1

\int_{0}^{4} \frac{x}{4} d x

\int_{- \infty}^{2} \frac{1}{x ^{2} + 4} d x

\int_{1}^{5} (2 x - 5)^{3} d x

\int_{0}^{1} \frac{1}{4 t} + 9 d t

\int_{1}^{2} e^{x} d x

What is the integral from-3 to 2 of e^{x+3} ?
The integral from-3 to 2 of e^{x+3} is e^5-1