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Popular Calculus >

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

Graph

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

integral of x^5ln(7x^3)

\int x^{5} ln (7 x^{3}) 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