What is the integral from 0 to 4 of 2(3)^x ?

The integral from 0 to 4 of 2(3)^x is (160)/(ln(3))

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integral from 0 to 4 of 2(3)^x

\int_{0}^{4} 2 (3)^{x} d x

\frac{160}{ln ( 3 )}

Decimal

145.63827 \dots

Solution steps

\int_{0}^{4} 2 \cdot 3^{x} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{4} 3^{x} d x

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

= 2 [\frac{3 ^{x}}{ln ( 3 )}]_{0}^{4}

Compute the boundaries:

\frac{80}{ln ( 3 )}

= 2 \cdot \frac{80}{ln ( 3 )}

Simplify

= \frac{160}{ln ( 3 )}

\int_{1}^{2} x^{2} + \frac{1}{x ^{2}} d x

\int_{0}^{1} 4 - 2 x^{2} d x

\int_{0}^{2} (x - 3)^{3} d x

\int_{1}^{2} 3 - x - \frac{2}{x} d x

\int_{2}^{x} (t^{3} + 4 t - 2) d t

What is the integral from 0 to 4 of 2(3)^x ?
The integral from 0 to 4 of 2(3)^x is (160)/(ln(3))