What is the integral from 11 to 2005 of x^4-2cos(x) ?

The integral from 11 to 2005 of x^4-2cos(x) is 401^5*625-161051/5-2(sin(2005)-sin(11))

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integral from 11 to 2005 of x^4-2cos(x)

\int_{11}^{2005} x^{4} - 2 cos (x) d x

40 1^{5} \cdot 625 - \frac{161051}{5} - 2 (sin (2005) - sin (11))

Decimal Notation

6.4804 E 15

Solution steps

\int_{11}^{2005} x^{4} - 2 cos (x) 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_{11}^{2005} x^{4} d x - \int_{11}^{2005} 2 cos (x) d x

\int_{11}^{2005} x^{4} d x = 40 1^{5} \cdot 625 - \frac{161051}{5}

\int_{11}^{2005} 2 cos (x) d x = 2 (sin (2005) - sin (11))

= 40 1^{5} \cdot 625 - \frac{161051}{5} - 2 (sin (2005) - sin (11))

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What is the integral from 11 to 2005 of x^4-2cos(x) ?
The integral from 11 to 2005 of x^4-2cos(x) is 401^5*625-161051/5-2(sin(2005)-sin(11))