What is the integral from 0 to 10 of (t^2)/2+4t+5 ?

The integral from 0 to 10 of (t^2)/2+4t+5 is 1250/3

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integral from 0 to 10 of (t^2)/2+4t+5

\int_{0}^{10} \frac{t ^{2}}{2} + 4 t + 5 d t

\frac{1250}{3}

Decimal Notation

416.66666 \dots

Solution steps

\int_{0}^{10} \frac{t ^{2}}{2} + 4 t + 5 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_{0}^{10} \frac{t ^{2}}{2} d t + \int_{0}^{10} 4 t d t + \int_{0}^{10} 5 d t

\int_{0}^{10} \frac{t ^{2}}{2} d t = \frac{500}{3}

\int_{0}^{10} 4 t d t = 200

\int_{0}^{10} 5 d t = 50

= \frac{500}{3} + 200 + 50

Simplify

\frac{500}{3} + 200 + 50 : \frac{1250}{3}

= \frac{1250}{3}

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What is the integral from 0 to 10 of (t^2)/2+4t+5 ?
The integral from 0 to 10 of (t^2)/2+4t+5 is 1250/3