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Popular Calculus >

integral of (t-1)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

\int 1 d t = t

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

Add a constant to the solution

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

Graph

Popular Examples

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\int sin^{8} (x) cos^{7} (x) d x

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

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

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

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

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

integral of x^2e^{x/4}

\int x^{2} e^{\frac{x}{4}} d x

Frequently Asked Questions (FAQ)

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