What is the integral from 0 to 2 of 20000e^{0.03x} ?

The integral from 0 to 2 of 20000e^{0.03x} is 41224.36436…

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integral from 0 to 2 of 20000e^{0.03x}

\int_{0}^{2} 20000 e^{0.03 x} d x

41224.36436 \dots

Solution steps

\int_{0}^{2} 20000 e^{0.03 x} d x

Take the constant out:

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

= 20000 \cdot \int_{0}^{2} e^{0.03 x} d x

Apply u-substitution

: \int_{0}^{0.06} e^{u} \frac{1}{0.03} d u

= 20000 \cdot \int_{0}^{0.06} e^{u} \frac{1}{0.03} d u

Take the constant out:

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

= 20000 \cdot \frac{1}{0.03} \cdot \int_{0}^{0.06} e^{u} d u

Simplify

= 20000 \cdot 33.33333 \dots \cdot \int_{0}^{0.06} e^{u} d u

Use the common integral:

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

= 20000 \cdot 33.33333 \dots [e^{u}]_{0}^{0.06}

Simplify

= 666666.66666 \dots [e^{u}]_{0}^{0.06}

Compute the boundaries:

0.06183 \dots

= 666666.66666 \dots \cdot 0.06183 \dots

Simplify

= 41224.36436 \dots

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What is the integral from 0 to 2 of 20000e^{0.03x} ?
The integral from 0 to 2 of 20000e^{0.03x} is 41224.36436…