What is the integral from 11 to 12.5 of 3e^{-3x} ?

The integral from 11 to 12.5 of 3e^{-3x} is 4.60713E-15

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integral from 11 to 12.5 of 3e^{-3x}

\int_{11}^{12.5} 3 e^{- 3 x} d x

4.60713 E - 15

Solution steps

\int_{11}^{12.5} 3 e^{- 3 x} d x

Take the constant out:

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

= 3 \cdot \int_{11}^{12.5} e^{- 3 x} d x

Apply u-substitution

: \int_{- 33}^{- 37.5} - \frac{1}{3} e^{u} d u

= 3 \cdot \int_{- 33}^{- 37.5} - \frac{1}{3} e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 3 (- \int_{- 37.5}^{- 33} - \frac{1}{3} e^{u} d u)

Take the constant out:

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

= 3 (- (- \frac{1}{3} \cdot \int_{- 37.5}^{- 33} e^{u} d u))

Use the common integral:

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

= 3 (- (- \frac{1}{3} [e^{u}]_{- 37.5}^{- 33}))

Simplify

3 (- (- \frac{1}{3} [e^{u}]_{- 37.5}^{- 33})) : [e^{u}]_{- 37.5}^{- 33}

= [e^{u}]_{- 37.5}^{- 33}

Compute the boundaries:

4.60713 E - 15

= 4.60713 E - 15

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What is the integral from 11 to 12.5 of 3e^{-3x} ?
The integral from 11 to 12.5 of 3e^{-3x} is 4.60713E-15