What is the integral from-2.5 to 0 of e^{3x} ?

The integral from-2.5 to 0 of e^{3x} is 0.33314…

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integral from-2.5 to 0 of e^{3x}

\int_{- 2.5}^{0} e^{3 x} d x

0.33314 \dots

Solution steps

\int_{- 2.5}^{0} e^{3 x} d x

Apply u-substitution

= \int_{- 7.5}^{0} e^{u} \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{- 7.5}^{0} e^{u} d u

Use the common integral:

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

= \frac{1}{3} [e^{u}]_{- 7.5}^{0}

Simplify

= 0.33333 \dots [e^{u}]_{- 7.5}^{0}

Compute the boundaries:

0.99944 \dots

= 0.33333 \dots \cdot 0.99944 \dots

Simplify

= 0.33314 \dots

What is the integral from-2.5 to 0 of e^{3x} ?
The integral from-2.5 to 0 of e^{3x} is 0.33314…