What is the integral from 9 to 10 of (x-10)^9 ?

The integral from 9 to 10 of (x-10)^9 is -(9^{10})/(10)+348678440

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integral from 9 to 10 of (x-10)^9

\int_{9}^{10} (x - 10)^{9} d x

- \frac{9 ^{10}}{10} + 348678440

Decimal

- 0.10000 \dots

Solution steps

\int_{9}^{10} (x - 10)^{9} d x

Expand

(x - 10)^{9} : x^{9} - 90 x^{8} + 3600 x^{7} - 84000 x^{6} + 1260000 x^{5} - 12600000 x^{4} + 84000000 x^{3} - 360000000 x^{2} + 900000000 x - 1000000000

= \int_{9}^{10} x^{9} - 90 x^{8} + 3600 x^{7} - 84000 x^{6} + 1260000 x^{5} - 12600000 x^{4} + 84000000 x^{3} - 360000000 x^{2} + 900000000 x - 1000000000 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_{9}^{10} x^{9} d x - \int_{9}^{10} 90 x^{8} d x + \int_{9}^{10} 3600 x^{7} d x - \int_{9}^{10} 84000 x^{6} d x + \int_{9}^{10} 1260000 x^{5} d x - \int_{9}^{10} 12600000 x^{4} d x + \int_{9}^{10} 84000000 x^{3} d x - \int_{9}^{10} 360000000 x^{2} d x + \int_{9}^{10} 900000000 x d x - \int_{9}^{10} 1000000000 d x

\int_{9}^{10} x^{9} d x = 1000000000 - \frac{9 ^{10}}{10}

\int_{9}^{10} 90 x^{8} d x = 6125795110

\int_{9}^{10} 3600 x^{7} d x = 25628975550

\int_{9}^{10} 84000 x^{6} d x = 62604372000

\int_{9}^{10} 1260000 x^{5} d x = 98397390000

\int_{9}^{10} 12600000 x^{4} d x = 103196520000

\int_{9}^{10} 84000000 x^{3} d x = 72219000000

\int_{9}^{10} 360000000 x^{2} d x = 32520000000

\int_{9}^{10} 900000000 x d x = 8550000000

\int_{9}^{10} 1000000000 d x = 1000000000

= 1000000000 - \frac{9 ^{10}}{10} - 6125795110 + 25628975550 - 62604372000 + 98397390000 - 103196520000 + 72219000000 - 32520000000 + 8550000000 - 1000000000

Simplify

= - \frac{9 ^{10}}{10} + 348678440

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What is the integral from 9 to 10 of (x-10)^9 ?
The integral from 9 to 10 of (x-10)^9 is -(9^{10})/(10)+348678440