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Popular >

integral of (y-1)^2

Solution

\int (y - 1)^{2} d y

Solution

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

Solution steps

\int (y - 1)^{2} d y

Expand

(y - 1)^{2} : y^{2} - 2 y + 1

= \int y^{2} - 2 y + 1 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 2 y d y + \int 1 d y

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

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

\int 1 d y = y

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial x)(4ye^x)

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d/(dθ)(tan(θ))

\frac{d}{d θ} (tan (θ))

derivative of x*y

\frac{d}{d x} (x \cdot y)

derivative of (ln(cos^2(x))^2)

\frac{d}{d x} ((ln (cos^{2} (x)))^{2})

area 3(x^3-x),0,-1,0 area

3 (x^{3} - x), 0, - 1, 0

Frequently Asked Questions (FAQ)

What is the integral of (y-1)^2 ?
The integral of (y-1)^2 is (y^3)/3-y^2+y+C