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Popular >

integral of (1-y)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

\int 1 d y = y

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

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

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

Add a constant to the solution

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

Popular Examples

integral of 1/(7-x^2)

\int \frac{1}{7 - x ^{2}} d x

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

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

integral of (tan(x))/(sec(x)+cos(x))

\int \frac{tan ( x )}{sec ( x ) + cos ( x )} d x

integral of (cos(β))/(2+3sin(β))

\int \frac{cos ( β )}{2 + 3 sin ( β )} d β

integral of (x+1)/(x^2+5x+6)

\int \frac{x + 1}{x ^{2} + 5 x + 6} d x

Frequently Asked Questions (FAQ)

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