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

The integral of (200+t)^2 is 40000t+200t^2+(t^3)/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (200+t)^2

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

40000 t + 200 t^{2} + \frac{t ^{3}}{3} + C

Solution steps

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

Expand

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

= \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

= \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}

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

Add a constant to the solution

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

What is the integral of (200+t)^2 ?
The integral of (200+t)^2 is 40000t+200t^2+(t^3)/3+C