What is the integral from 3 to 6 of 10^8((t^2)/3+1) ?

The integral from 3 to 6 of 10^8((t^2)/3+1) is 2400000000

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integral from 3 to 6 of 10^8((t^2)/3+1)

\int_{3}^{6} 1 0^{8} (\frac{t ^{2}}{3} + 1) d t

2400000000

Solution steps

\int_{3}^{6} 1 0^{8} (\frac{t ^{2}}{3} + 1) d t

Take the constant out:

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

= 1 0^{8} \cdot \int_{3}^{6} \frac{t ^{2}}{3} + 1 d t

Simplify

= 100000000 \cdot \int_{3}^{6} \frac{t ^{2}}{3} + 1 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

= 100000000 (\int_{3}^{6} \frac{t ^{2}}{3} d t + \int_{3}^{6} 1 d t)

\int_{3}^{6} \frac{t ^{2}}{3} d t = 21

\int_{3}^{6} 1 d t = 3

= 100000000 (21 + 3)

Simplify

= 2400000000

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What is the integral from 3 to 6 of 10^8((t^2)/3+1) ?
The integral from 3 to 6 of 10^8((t^2)/3+1) is 2400000000