anonymous
  • anonymous
How do I solve the integral of x(x-10)^10?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
do a substitution with u=10-x
anonymous
  • anonymous
sorry kill that u=x-10 that should say
anonymous
  • anonymous
du/dx = 1

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anonymous
  • anonymous
wait
anonymous
  • anonymous
that wont work
anonymous
  • anonymous
this isnt hard
anonymous
  • anonymous
use binomial formula to expand (x-10)^10
anonymous
  • anonymous
no i see the problem, yeah it seemed to easy
anonymous
  • anonymous
integral x [ x^10 + 10 choose 1 x^9 (-1) + 10 choose 2 x^8 * (-1)^2 + ...
anonymous
  • anonymous
make a pascal triangle
anonymous
  • anonymous
here http://www.twiddla.com/491685
anonymous
  • anonymous
online whiteboard
anonymous
  • anonymous
i think you should be able to use the substitution u=x-10 du/dx = 1 so this is the integral of (u+10)u^10 which is simply u^11 +10u^10 so this gives soln (u^12)/12 +10(u^11)/11 and then put x back in for u
anonymous
  • anonymous
oh
anonymous
  • anonymous
You have to use a complex substitution: \[\int\limits_{}^{} x(x-10)^{10} dx\] u = x-10 x = u + 10, dx = 1 du Substitute and profit!
anonymous
  • anonymous
how about integral x^2 (x-10)^10
anonymous
  • anonymous
it doesn't have to be complex this problem is purely in the reals
anonymous
  • anonymous
ac, right. i think he meant . wrong choice of words
anonymous
  • anonymous
Oh, I meant complex as in 'difficult', lol.
anonymous
  • anonymous
hehe
anonymous
  • anonymous
i became both of you guys fans
anonymous
  • anonymous
acland, it would be much tougher if you had to do integral x^10 (x-10)^10 dx
anonymous
  • anonymous
then there is no avoiding pascal's beautiful triangle
anonymous
  • anonymous
bad choice of words, you get to used to dealing with complex number systems all the time. For the x^2 one you should be able to use the same idea and have the integral of \[(u+10)^2+u^{10}\] yeah if it was x^10 then you would have to look at other ways of solving it
anonymous
  • anonymous
u = x-10 du = dx u + 10 = x so int (u+10) u^10
anonymous
  • anonymous
if it was x^10 i just wouldnt bother and would leave my final answer as an integral
anonymous
  • anonymous
so int u^11 + 10 u^10
anonymous
  • anonymous
i got a toughie
anonymous
  • anonymous
A tract of land bordered by a highway along the y-axis, a dirt road along the x-axis, and a river whose path is given by the equation y=4-0.2x^2, where x and y are in hindreds of meters. The tract is 300m deep along the dirt road The value of the land is constant in any strip parallel to the highway and increases as you move way from the highway, with the value given by v=1000+50x dollars per 10,000 m^2 at the sample point (x,y). Find dW, the worth of a strip. Write an integral that equals the worth of the entire tract.
anonymous
  • anonymous
i thought about using a double integral

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