What is the integral from 0 to 10 of-6.4(0.9^x) ?

The integral from 0 to 10 of-6.4(0.9^x) is -39.56375…

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integral from 0 to 10 of-6.4(0.9^x)

\int_{0}^{10} - 6.4 (0. 9^{x}) d x

- 39.56375 \dots

Solution steps

\int_{0}^{10} - 6.4 \cdot 0. 9^{x} d x

Take the constant out:

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

= - 6.4 \cdot \int_{0}^{10} 0. 9^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= - 6.4 [\frac{0. 9 ^{x}}{ln ( 0.9 )}]_{0}^{10}

\frac{0. 9 ^{x}}{ln ( 0.9 )} = - 9.49122 \dots \cdot 0. 9^{x}

= - 6.4 [- 9.49122 \dots \cdot 0. 9^{x}]_{0}^{10}

Compute the boundaries:

6.18183 \dots

= - 6.4 \cdot 6.18183 \dots

Simplify

= - 39.56375 \dots

What is the integral from 0 to 10 of-6.4(0.9^x) ?
The integral from 0 to 10 of-6.4(0.9^x) is -39.56375…