Homework Statement
An ideal gas expands isothermally, performing 3.40x10^3 J of work in the process.
a) The change in internal energy of the gas
b) The heat absorbed during this expansion
Homework Equations
\DeltaU=Q-W
The Attempt at a Solution
a) Since it's isothermally...
Homework Statement
y'=xsec^2(x^2)
2. The attempt at a solution
dy/dx=xsec^2(x^2)
dy=xsec^2(x^2)dx
\intdy=\intxsec^2(x^2)dx
lny= (here i'll do a u substitution)
----
u=x^2 du=1/3x^3dx
... and here's my problem. It seems like that creates a very difficult u-sub to try and manage...
oh wow, that's what i get for trying to do calculus late at night. i was trying to evaluate an integral after i already evaluated it. so my final answer was correct... just need to watch out and make sure i drop the integral sign.
should have been...
(1/6)(4/5)u^5/4
2/15(3x^2+5)^5/4+C
thank...
no, they wouldn't be equal. for example, does 5=0.5(5)^2? no; 5 does not equal 12.5
did i pull my denominator up incorrectly? if (x^n+1/n+1) is (x^.25+1/.25+1), then (x^1.25/1.25). so to pull up the denominator...
i was trying to use the power rule for integrals (x^n+1/n+1). but i have a feeling i can't do that. haha :)
then i pulled the 1/6 back into it and multiplied it out (1/6 times 4/5=2/15).
Homework Statement
\intx(3x^2+5)^1/4
2. The attempt at a solution
u=3x^2+5 du=6x
1/6\int6x(3x^2+5)^1/4
this is where I'm getting sloppy, i think...
1/6\intdu(u)^1/4
1/6\int4/5(u)^5/4
\int2/15(3x^2+5)^5/4
and then i get stuck.
\int xsec^2xdx
u=x du=dx dv=sec^2xdx v=tanx
uv- \intvdu
xtanx-\inttanxdx
xtanx-lnlcosxl+C
just wanted to make sure everything looked alright because I am not feeling totally confident about my last step.
Homework Statement
The apparent weight a person feels is the normal force that acts on the person. Suppose a Ferris Wheel has a diameter of 28.om and makes one revolution every 13.3 seconds. What is the ratio of a person's apparent weight to real weight a) at the top and b) at the bottom...