Question

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

Answer 1

do a substitution with u=10-x

Answer 2

sorry kill that u=x-10 that should say

Answer 3

du/dx = 1

Answer 4

wait

Answer 5

that wont work

Answer 6

this isnt hard

Answer 7

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

Answer 8

no i see the problem, yeah it seemed to easy

Answer 9

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

Answer 10

make a pascal triangle

Answer 11

here http://www.twiddla.com/491685

Answer 12

online whiteboard

Answer 13

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

Answer 14

oh

Answer 15

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!

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

hehe

Answer 21

i became both of you guys fans

Answer 22

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

Answer 23

then there is no avoiding pascal's beautiful triangle

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

so int u^11 + 10 u^10

Answer 28

i got a toughie

Answer 29

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.

Answer 30

i thought about using a double integral