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

- anonymous

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

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

do a substitution with u=10-x

- anonymous

sorry kill that u=x-10 that should say

- anonymous

du/dx = 1

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

wait

- anonymous

that wont work

- anonymous

this isnt hard

- anonymous

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

- anonymous

no i see the problem, yeah it seemed to easy

- anonymous

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

- anonymous

make a pascal triangle

- anonymous

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

- anonymous

online whiteboard

- 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

oh

- 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

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

hehe

- anonymous

i became both of you guys fans

- anonymous

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

- anonymous

then there is no avoiding pascal's beautiful triangle

- 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

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

- anonymous

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

- anonymous

so int u^11 + 10 u^10

- anonymous

i got a toughie

- 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

i thought about using a double integral

Looking for something else?

Not the answer you are looking for? Search for more explanations.