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Popular Calculus >

integral of (y-4)^2

Solution

\int (y - 4)^{2} d y

Solution

\frac{y ^{3}}{3} - 4 y^{2} + 16 y + C

Solution steps

\int (y - 4)^{2} d y

Expand

(y - 4)^{2} : y^{2} - 8 y + 16

= \int y^{2} - 8 y + 16 d y

Apply the Sum Rule:

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

= \int y^{2} d y - \int 8 y d y + \int 16 d y

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

\int 8 y d y = 4 y^{2}

\int 16 d y = 16 y

= \frac{y ^{3}}{3} - 4 y^{2} + 16 y

Add a constant to the solution

= \frac{y ^{3}}{3} - 4 y^{2} + 16 y + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (y-4)^2 ?
The integral of (y-4)^2 is (y^3)/3-4y^2+16y+C