What is the integral from 0 to 1 of 100e^{-0.01t} ?

The integral from 0 to 1 of 100e^{-0.01t} is 99.50166…

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integral from 0 to 1 of 100e^{-0.01t}

\int_{0}^{1} 100 e^{- 0.01 t} d t

99.50166 \dots

Solution steps

\int_{0}^{1} 100 e^{- 0.01 t} d t

Take the constant out:

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

= 100 \cdot \int_{0}^{1} e^{- 0.01 t} d t

Apply u-substitution

: \int_{0}^{- 0.01} - \frac{1}{0.01} e^{u} d u

= 100 \cdot \int_{0}^{- 0.01} - \frac{1}{0.01} e^{u} d u

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

= 100 (- \int_{- 0.01}^{0} - \frac{1}{0.01} e^{u} d u)

Take the constant out:

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

= 100 (- (- \frac{1}{0.01} \cdot \int_{- 0.01}^{0} e^{u} d u))

Simplify

= 100 (- (- 100 \cdot \int_{- 0.01}^{0} e^{u} d u))

Use the common integral:

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

= 100 (- (- 100 [e^{u}]_{- 0.01}^{0}))

Simplify

= 10000 [e^{u}]_{- 0.01}^{0}

Compute the boundaries:

0.00995 \dots

= 10000 \cdot 0.00995 \dots

Simplify

= 99.50166 \dots

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What is the integral from 0 to 1 of 100e^{-0.01t} ?
The integral from 0 to 1 of 100e^{-0.01t} is 99.50166…