What is the integral of (100-x)^2 ?

The integral of (100-x)^2 is 10000x-100x^2+(x^3)/3+C

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integral of (100-x)^2

\int (100 - x)^{2} d x

10000 x - 100 x^{2} + \frac{x ^{3}}{3} + C

Solution steps

\int (100 - x)^{2} d x

Expand

(100 - x)^{2} : 10000 - 200 x + x^{2}

= \int 10000 - 200 x + x^{2} d x

Apply the Sum Rule:

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

= \int 10000 d x - \int 200 x d x + \int x^{2} d x

\int 10000 d x = 10000 x

\int 200 x d x = 100 x^{2}

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

= 10000 x - 100 x^{2} + \frac{x ^{3}}{3}

Add a constant to the solution

= 10000 x - 100 x^{2} + \frac{x ^{3}}{3} + C

What is the integral of (100-x)^2 ?
The integral of (100-x)^2 is 10000x-100x^2+(x^3)/3+C