What is the integral of 3(200+t)^2 ?

The integral of 3(200+t)^2 is 120000t+600t^2+t^3+C

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integral of 3(200+t)^2

\int 3 (200 + t)^{2} d t

120000 t + 600 t^{2} + t^{3} + C

Solution steps

\int 3 (200 + t)^{2} d t

Take the constant out:

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

= 3 \cdot \int (200 + t)^{2} d t

Expand

(200 + t)^{2} : 40000 + 400 t + t^{2}

= 3 \cdot \int 40000 + 400 t + t^{2} 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

= 3 (\int 40000 d t + \int 400 t d t + \int t^{2} d t)

\int 40000 d t = 40000 t

\int 400 t d t = 200 t^{2}

\int t^{2} d t = \frac{t ^{3}}{3}

= 3 (40000 t + 200 t^{2} + \frac{t ^{3}}{3})

Simplify

3 (40000 t + 200 t^{2} + \frac{t ^{3}}{3}) : 120000 t + 600 t^{2} + t^{3}

= 120000 t + 600 t^{2} + t^{3}

Add a constant to the solution

= 120000 t + 600 t^{2} + t^{3} + C

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What is the integral of 3(200+t)^2 ?
The integral of 3(200+t)^2 is 120000t+600t^2+t^3+C