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Popular >

integral of (3-x)^2

Solution

\int (3 - x)^{2} d x

Solution

9 x - 3 x^{2} + \frac{x ^{3}}{3} + C

Solution steps

\int (3 - x)^{2} d x

Expand

(3 - x)^{2} : 9 - 6 x + x^{2}

= \int 9 - 6 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 9 d x - \int 6 x d x + \int x^{2} d x

\int 9 d x = 9 x

\int 6 x d x = 3 x^{2}

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

= 9 x - 3 x^{2} + \frac{x ^{3}}{3}

Add a constant to the solution

= 9 x - 3 x^{2} + \frac{x ^{3}}{3} + C

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\int_{0}^{5} 5 x d x

Frequently Asked Questions (FAQ)

What is the integral of (3-x)^2 ?
The integral of (3-x)^2 is 9x-3x^2+(x^3)/3+C