Homework Statement
The function is increasing and has a inverse f^-1
Also assume f′is continuous and f'(x) > 0 over the state interval of integration [a,b]
PLEASE NOTE! a is lower limit, b is upper limit (same for alpha and beta symbol later on)
Used integration by parts to show that:
\int...
Homework Statement
Evaulate the following integral:
2*integral from r-b to r of h(x-r+b)b*sqrt(r2-x2) dx
or a picture
http://imgur.com/n2PUN
Homework Equations
The Attempt at a Solution
Tried setting u = r^2-x^2, lost after a couple more steps. Nothing seems to cancel out smoothly. For the...
Homework Statement
Show and prove that where u < -a:
integral of 1/(sqrt(u^2-a^2)) = ln(u+sqrt(u^2-a^2))+C or -cosh^-1(-u/a)+C
Homework Equations
when u > a, the
integral of 1/(sqrt(u^2-a^2)) = ln(u+sqrt(u^2-a^2))+C or -cosh^-1(-u/a)+C
My attempt at a solution: Don't I just use the same...
Homework Statement
A cathedral dome is designed with three semi circular supports of radius r so that each horiontal cross section is a regular hexagon. Show that the volume of the dome is r^3 * sqrt(3)
an accompanying figure - http://imgur.com/3fSqh
Homework Equations...
Homework Statement
See the bottom problem (#2)
See image - http://imageshack.us/photo/my-images/842/img7774y.jpg/
The Attempt at a Solution
Plugged in 2 for f(x) and -4^2 for g^2(x)
got 2/3,
Is this correct? All help appreciated! Mad at my Calc teacher because he never gave us...