# Search results

1. ### A simple question

i just finished calculus bc ap at my school, and i have no more math classes to take there; i need all 4 years of math to graduate with honors :confused: . im planning on taking a college course in math next year, but i dont know what math course to take. i was wondering if any of you had any...
2. ### Tricky trig substitution

im hoping i worked this out right; its long: \int x(81-x^2)^{5/2}dx the integral contains a^2-x^2, so i set x=asin\theta. that would make x=9sin\theta and dx=9cos\theta d\theta: \int 9sin\theta(81-81sin^2\theta)^{5/2}9cos\theta d\theta = \int 9sin\theta[81(1-sin^2\theta)]^{5/2}9cos\theta...
3. ### Quartic equation

this was on the aime, and i was wondering how to factor it without a calculator. x^4-4x^3+6x^2-4x=2005
4. ### Challenging problems

Six congruent circles form a ring with each circle externally tangent to two circles adjacent to it. All six circles are internally tangent to a circle C with radius 30. Let K be the area of the region inside C and outside all of the six circles in the ring. Find |K|. (The notation |K|...
5. ### Initial value problem

\frac{dy}{dx}=x-4-xy-4y you are given that y(0)=4. so, here's what i did: \frac{dy}{dx}=(x-4)(y+1) \frac{dy}{y+1}=(x-4)dx i integrated both sides: ln(y+1)=\frac{x^2}{2}-4x+C y=e^{\frac{x^2}{2}}e^{-4x}e^{C}-1 plugged in for x and y: 4=e^{\frac{0^2}{x}}e^{-4*0}e^{C}-1 5=e^C...
6. ### Velocity and what not

i had this problem on my calculus test the other day that was actually challenging. the whole class tried to get it taken off of the test, because barely any of them did it. :sad: i was wanting to know if i approached it right and yielded the correct answer. given v(t)=13e^{-.02t}sin(t)...
7. ### Self teaching Multivariable calculus

hello, i was wanting to teach myself multivariable calculus. i am currently in calculus BC AP. that class isnt challenging enough for me. do any of you out there know any good sites or good books for multivariable calculus. any help would be greatly apprecaited. thanks in advance.