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Popular >

integral of (12-x)^2

Solution

\int (12 - x)^{2} d x

Solution

144 x - 12 x^{2} + \frac{x ^{3}}{3} + C

Solution steps

\int (12 - x)^{2} d x

Expand

(12 - x)^{2} : 144 - 24 x + x^{2}

= \int 144 - 24 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 144 d x - \int 24 x d x + \int x^{2} d x

\int 144 d x = 144 x

\int 24 x d x = 12 x^{2}

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

= 144 x - 12 x^{2} + \frac{x ^{3}}{3}

Add a constant to the solution

= 144 x - 12 x^{2} + \frac{x ^{3}}{3} + C

Graph

Popular Examples

integral of (1-x)^2sqrt(x+2)

\int (1 - x)^{2} x + 2 d x

integral of 1/(2^{3x)}

\int \frac{1}{2 ^{3 x}} d x

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integral of x^2(2x^3+3)^5

\int x^{2} (2 x^{3} + 3)^{5} d x

integral of 1/(sqrt(tan^2(x)))

\int \frac{1}{tan ^{2} ( x )} d x

Frequently Asked Questions (FAQ)

What is the integral of (12-x)^2 ?
The integral of (12-x)^2 is 144x-12x^2+(x^3)/3+C