How do I solve the integral of x(x-10)^10?

do a substitution with u=10-x

sorry kill that u=x-10 that should say

du/dx = 1

wait

that wont work

this isnt hard

use binomial formula to expand (x-10)^10

no i see the problem, yeah it seemed to easy

integral x [ x^10 + 10 choose 1 x^9 (-1) + 10 choose 2 x^8 * (-1)^2 + ...

make a pascal triangle

online whiteboard

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

oh

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!

how about integral x^2 (x-10)^10

it doesn't have to be complex this problem is purely in the reals

ac, right. i think he meant . wrong choice of words

Oh, I meant complex as in 'difficult', lol.

hehe

i became both of you guys fans

acland, it would be much tougher if you had to do integral x^10 (x-10)^10 dx

then there is no avoiding pascal's beautiful triangle

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

u = x-10 du = dx u + 10 = x so int (u+10) u^10

if it was x^10 i just wouldnt bother and would leave my final answer as an integral

so int u^11 + 10 u^10

i got a toughie

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.

i thought about using a double integral

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