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Popular >

integral from 6 to 9 of (x-7)^2

Solution

\int_{6}^{9} (x - 7)^{2} d x

Solution

3

Solution steps

\int_{6}^{9} (x - 7)^{2} d x

Expand

(x - 7)^{2} : x^{2} - 14 x + 49

= \int_{6}^{9} x^{2} - 14 x + 49 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_{6}^{9} x^{2} d x - \int_{6}^{9} 14 x d x + \int_{6}^{9} 49 d x

\int_{6}^{9} x^{2} d x = 171

\int_{6}^{9} 14 x d x = 315

\int_{6}^{9} 49 d x = 147

= 171 - 315 + 147

Simplify

= 3

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x \to 3 lim (x^{2} + 1)

integral of-t/2

\int - \frac{t}{2} d t

Frequently Asked Questions (FAQ)

What is the integral from 6 to 9 of (x-7)^2 ?
The integral from 6 to 9 of (x-7)^2 is 3