The question I'm working on is "use the appropriate Trigonometric substitution to evaluate the following integral: \int \frac{x^2}{(4x^2-49)^\frac{3}{2}}dx " Now the first thing i did was make it so that it had a root in it by making it \int \frac{x^2}{(4x^2-49)(4x^2-49)^\frac{1}{2}}dx
this...
can anyone see what the book did(i would like to get it solved the same way they did it.) up to the point where it subs in v i can see what they did, but when i sub in v i get \int_{\sqrt{2}}^{\sqrt{1+e^2}} \frac{v^2}{(v^2-1)^2} dv and don't know how they got the roots of it.
and even then i...
yeah, i am seeing that...the book jumps from \int_{1}^{e} \frac{\sqrt{1+u^2}}{u^2}u du to \int_{\sqrt{2}}^{\sqrt{1+e^2}} \frac{v}{(v^2-1)} dv and (without checking) i figured \frac{x^2}{y^2}=\frac{x}{y} my mistake. now I'm really confused, because i see how they get \int_{1}^{e}...
my problem is to find the arc length of y=e^x between 0 and 1
what I've got is \int_{0}^{1} \sqrt{1+(e^x)^2}dx which i then substitute u=e^x giving \int_{1}^{e} \frac{\sqrt{1+u^2}}{u^2}u du which i then sub in v=\sqrt{1+u^2} giving \int_{\sqrt{2}}^{\sqrt{1+e^2}} \frac{v^2}{(v^2-1)^2} dv =...
the question i have in my assignment is this :
"Find the volume common to two circular cylinders each with radius r if the axes of the cylinders intersect at right angles"
now, I'm not even sure what they're asking, let alone where to begin.
not looking for answers, just a nudge in the...
I'm coming to a realization that i really don't get how to do integrals.
i understand the basic concept, it's an anti-derivative. when you evaluate them, you sub in the values that you want to evaluate, and subtract them bottom from top.
i also understand that when you integrate, you get...
Q:What is the coefficient of friction of a cat?
A: Mu
Q:What is the maximum speed a computer can attain falling through an atmosphere?
A:Terminal velocity.
but at the same time, the stuff you learn in later classes essentially forces you to understand what was happening in the previous ones.
for example, for some reason i had a real blank with logs when i took grade 12 math, but now I'm 4/5ths the way through calc I, and i have no trouble with...
ok, so I'm doing a calc assignment, and the whole assignment is done except for one question, the rest of the answers check properly on my graphing calculator both with nDeriv and the tangent function. this question shouldn't be so hard, but i must be missing something. could use a bit of help...
basically what you would want to do there, since you already know two of the dimensions of the volume(length=1m and width=1m), is figure out what the 100,000N is in kg and divide that by how many kilos it is per m^3. because you have a 1x1 square, the number of cubic meters will also be the...
bobg: noticed a slight problem with that method. would need to get a third formula for the time because of the (at)*(.5)(t). you're able to substitute out the at, but there's still a t in there that you would need to deal with.
the reason i chose the formula i did was because the only...
another approach would be to figure out the average acceleration of the shot using v^2=v(initial)^2+2ad. from there finding the force is fairly simple.