What is the integral from 3 to 6 of (x^2-6x+9) ?

The integral from 3 to 6 of (x^2-6x+9) is 9

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integral from 3 to 6 of (x^2-6x+9)

\int_{3}^{6} (x^{2} - 6 x + 9) d x

9

Solution steps

\int_{3}^{6} x^{2} - 6 x + 9 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{3}^{6} x^{2} d x - \int_{3}^{6} 6 x d x + \int_{3}^{6} 9 d x

\int_{3}^{6} x^{2} d x = 63

\int_{3}^{6} 6 x d x = 81

\int_{3}^{6} 9 d x = 27

= 63 - 81 + 27

Simplify

= 9

\int_{0}^{l n (A)} 9 e^{3 x} d x

\int_{1}^{2} \frac{x}{3} d x

\int_{\frac{π}{6}}^{\frac{π}{3}} sin^{2} (x) d x

\int_{1}^{2} (3 x + 2) d x

\int_{0}^{2} t (2 t - 2) d t

What is the integral from 3 to 6 of (x^2-6x+9) ?
The integral from 3 to 6 of (x^2-6x+9) is 9