What is the integral from 0 to 1 of 1000*2^t ?

The integral from 0 to 1 of 1000*2^t is (1000)/(ln(2))

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integral from 0 to 1 of 1000*2^t

\int_{0}^{1} 1000 \cdot 2^{t} d t

\frac{1000}{ln ( 2 )}

Decimal

1442.69504 \dots

Solution steps

\int_{0}^{1} 1000 \cdot 2^{t} d t

Take the constant out:

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

= 1000 \cdot \int_{0}^{1} 2^{t} d t

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

= 1000 [\frac{2 ^{t}}{ln ( 2 )}]_{0}^{1}

Compute the boundaries:

\frac{1}{ln ( 2 )}

= 1000 \cdot \frac{1}{ln ( 2 )}

Simplify

= \frac{1000}{ln ( 2 )}

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What is the integral from 0 to 1 of 1000*2^t ?
The integral from 0 to 1 of 1000*2^t is (1000)/(ln(2))