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 March 13th, 2014, 02:43 PM #1 Newbie   Joined: Mar 2014 Posts: 1 Thanks: 0 Integral with lower and upper limits Hello everyone, I would be extremely grateful for your help with the following problem. I've been trying to solve this for the past hours and I cannot seem to arrive at the right answer :/ I'm trying to prepare for an exam in a week's time, but it's a hell of a problem. Could you please help me by explaining the process? Problem ( I will do my best to explain it as I can't write the symbols) (the upper and lower limits are the numbers for the f symbol, at the top and bottom of it) integral (F) *upper limit = 2, lower limit = 1; (x^2 - 1)^10 * 22x dx. So, the function looks like this: F (2=top, 1=bottom) (x^2 - 1)^10 * 22x dx. Please help! Aga
 March 13th, 2014, 10:26 PM #2 Senior Member   Joined: Mar 2014 Posts: 112 Thanks: 8 $\int(x^2\,-\,1)^{10}\,\ast\,22x\,dx\,=\,11\int2x(x^2\,-\,1)^{10}\,dx\,=\,(x^2\,-\,1)^{11}\,+\,C$ Using the fundamental theorem of calculus we get (2² - 1)^11 - (1² - 1)^11 = 3^11.
 March 14th, 2014, 06:49 AM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Integral with lower and upper limits $\int_1^2 (x^2- 1)^{10} 22xdx= 11\int_1^2 (x^2- 1)^{10} (2x dx)$ Let $u= x^2- 1$ so that $du= 1xdx$. When x= 1 u= 0, when x= 2, u= 3 so the integral becomes $11\int_0^1 u^{10} du= \left[u^{11}\right]_0^3= 3^{11}$

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