What is the integral from 0 to 6 of 2.3^tsin(t/2) ?

The integral from 0 to 6 of 2.3^tsin(t/2) is 96.61305…

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integral from 0 to 6 of 2.3^tsin(t/2)

\int_{0}^{6} 2. 3^{t} sin (\frac{t}{2}) d t

96.61305 \dots

Solution steps

\int_{0}^{6} 2. 3^{t} sin (\frac{t}{2}) d t

Compute the indefinite integral:

\int 2. 3^{t} sin (\frac{t}{2}) d t = - 0.52980 \dots \cdot 2. 3^{t} cos (0.5 t) + 0.88256 \dots \cdot 2. 3^{t} sin (0.5 t) + C

Compute the boundaries:

\int_{0}^{6} 2. 3^{t} sin (\frac{t}{2}) d t = 96.08324 \dots - (- 0.52980 \dots)

= 96.08324 \dots - (- 0.52980 \dots)

Simplify

= 96.61305 \dots

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What is the integral from 0 to 6 of 2.3^tsin(t/2) ?
The integral from 0 to 6 of 2.3^tsin(t/2) is 96.61305…