What is the integral from 0 to 2 of 10000e^{0.04x} ?

The integral from 0 to 2 of 10000e^{0.04x} is 20821.76691…

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integral from 0 to 2 of 10000e^{0.04x}

\int_{0}^{2} 10000 e^{0.04 x} d x

20821.76691 \dots

Solution steps

\int_{0}^{2} 10000 e^{0.04 x} d x

Take the constant out:

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

= 10000 \cdot \int_{0}^{2} e^{0.04 x} d x

Apply u-substitution

: \int_{0}^{0.08} e^{u} \frac{1}{0.04} d u

= 10000 \cdot \int_{0}^{0.08} e^{u} \frac{1}{0.04} d u

Take the constant out:

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

= 10000 \cdot \frac{1}{0.04} \cdot \int_{0}^{0.08} e^{u} d u

Simplify

= 10000 \cdot 25 \cdot \int_{0}^{0.08} e^{u} d u

Use the common integral:

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

= 10000 \cdot 25 [e^{u}]_{0}^{0.08}

Simplify

= 250000 [e^{u}]_{0}^{0.08}

Compute the boundaries:

0.08328 \dots

= 250000 \cdot 0.08328 \dots

Simplify

= 20821.76691 \dots

\int \frac{5 x ^{2} + 6 x + 9}{( x - 3 ) ^{2} ( x + 1 ) ^{2}} d x

\frac{d}{d x} (\frac{x ^{6}}{1 + x ^{12}})

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

\frac{\partial}{\partial y} (x^{2} + y^{2} - 25)

\int - 0.04 t d t

What is the integral from 0 to 2 of 10000e^{0.04x} ?
The integral from 0 to 2 of 10000e^{0.04x} is 20821.76691…