en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (t-2)^2

Solution

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

Solution

\frac{t ^{3}}{3} - 2 t^{2} + 4 t + C

Solution steps

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

Expand

(t - 2)^{2} : t^{2} - 4 t + 4

= \int t^{2} - 4 t + 4 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 t^{2} d t - \int 4 t d t + \int 4 d t

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

\int 4 t d t = 2 t^{2}

\int 4 d t = 4 t

= \frac{t ^{3}}{3} - 2 t^{2} + 4 t

Add a constant to the solution

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

Popular Examples

integral of tan(c)

\int tan (c)

integral of x/(sqrt(x^4+9))

\int \frac{x}{x ^{4} + 9} d x

integral of 3/(x^{1/3)}

\int \frac{3}{x ^{\frac{1}{3}}} d x

integral of (3x-3)/(x^2-2x+6)

\int \frac{3 x - 3}{x ^{2} - 2 x + 6} d x

integral of (1+cos(3x))^{3/2}

\int (1 + cos (3 x))^{\frac{3}{2}} d x

Frequently Asked Questions (FAQ)

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