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Popular >

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

Popular Examples

derivative of (x^2/(x-6))

\frac{d}{d x} (\frac{x ^{2}}{x - 6})

(\partial)/(\partial x)((xy)/(sqrt(1+xy^2)))

\frac{\partial}{\partial x} (\frac{x y}{1 + x y ^{2}})

integral of ((sin(x))^2)/((cos(x))^4)

\int \frac{( sin ( x ) ) ^{2}}{( cos ( x ) ) ^{4}} d x

integral from 1 to 4 of (e^{4/x})/(x^2)

\int_{1}^{4} \frac{e ^{\frac{4}{x}}}{x ^{2}} d x

derivative of ae^{2x}+be^x

\frac{d}{d x} (a e^{2 x} + b e^{x})

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