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Popular >

integral of (1-t)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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 t - \int 2 t d t + \int t^{2} d t

\int 1 d t = t

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

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

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

Add a constant to the solution

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

Popular Examples

derivative of (x^3-x(2x-x^2))

\frac{d}{d x} ((x^{3} - x) (2 x - x^{2}))

2y+(dy)/(dx)=y^2+1

2 y + \frac{d y}{d x} = y^{2} + 1

h(x)= 3/(x^2)+10x^3-2sin(3x)

h (x) = \frac{3}{x ^{2}} + 10 x^{3} - 2 sin (3 x)

integral of sqrt((2+3x)/(x-3))

\int \frac{2 + 3 x}{x - 3} d x

taylor ln(1-7x),0 taylor

ln (1 - 7 x), 0

Frequently Asked Questions (FAQ)

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