What is the integral from 3 to 7 of e^t-3t ?

The integral from 3 to 7 of e^t-3t is e^7-e^3-60

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integral from 3 to 7 of e^t-3t

\int_{3}^{7} e^{t} - 3 t d t

e^{7} - e^{3} - 60

Decimal

1016.54762 \dots

Solution steps

\int_{3}^{7} e^{t} - 3 t d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{3}^{7} e^{t} d t - \int_{3}^{7} 3 t d t

\int_{3}^{7} e^{t} d t = e^{7} - e^{3}

\int_{3}^{7} 3 t d t = 60

= e^{7} - e^{3} - 60

What is the integral from 3 to 7 of e^t-3t ?
The integral from 3 to 7 of e^t-3t is e^7-e^3-60