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

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

Popular >

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

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

e^{3} - 1

Decimal

19.08553 \dots

Solution steps

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

e^{x + 1} = e^{1} e^{x}

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

Take the constant out:

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

= e^{1} \cdot \int_{- 1}^{2} e^{x} d x

Simplify

= e \cdot \int_{- 1}^{2} e^{x} d x

Use the common integral:

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

= e [e^{x}]_{- 1}^{2}

Compute the boundaries:

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

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

Simplify

= e^{3} - 1

\int_{0}^{1} \frac{x}{1 + 6 x ^{2}} d x

\int_{0}^{4} (x^{2} + x) d x

\int_{1}^{3} (\frac{3}{4} x^{2} - 2) d x

\int_{0}^{5} (2 x - 1)^{2} d x

\int_{3}^{8.2} x^{2} - 10 x + 50 d x

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