What is the integral from 0 to 100 of e^{-x/(0.033)} ?

The integral from 0 to 100 of e^{-x/(0.033)} is 0.033(1-1/(e^{3030.30303…)})

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integral from 0 to 100 of e^{-x/(0.033)}

\int_{0}^{100} e^{- \frac{x}{0.033}} d x

0.033 (1 - \frac{1}{e ^{3030.30303 \dots}})

Solution steps

\int_{0}^{100} e^{- \frac{x}{0.033}} d x

Apply u-substitution

: \int_{0}^{- 3030.30303 \dots} - \frac{1}{30.30303 \dots} e^{u} d u

= \int_{0}^{- 3030.30303 \dots} - \frac{1}{30.30303 \dots} e^{u} d u

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

= - \int_{- 3030.30303 \dots}^{0} - \frac{1}{30.30303 \dots} e^{u} d u

Take the constant out:

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

= - (- \frac{1}{30.30303 \dots} \cdot \int_{- 3030.30303 \dots}^{0} e^{u} d u)

Simplify

= - (- 0.033 \cdot \int_{- 3030.30303 \dots}^{0} e^{u} d u)

Use the common integral:

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

= - (- 0.033 [e^{u}]_{- 3030.30303 \dots}^{0})

Simplify

= 0.033 [e^{u}]_{- 3030.30303 \dots}^{0}

Compute the boundaries:

1 - \frac{1}{e ^{3030.30303 \dots}}

= 0.033 (1 - \frac{1}{e ^{3030.30303 \dots}})

f (x) = (x^{3} - 2)^{3}

\frac{d}{d x} (x - 5 x^{2} + x^{3})

3 x^{2} + 3 x - 8, 2 x^{2} + x + 7

(3^{x})^{^{'}}

\frac{d}{d x} (cos (sin^{2} (x)))

What is the integral from 0 to 100 of e^{-x/(0.033)} ?
The integral from 0 to 100 of e^{-x/(0.033)} is 0.033(1-1/(e^{3030.30303…)})