4 replies to this topic

[jillian]

I coulda sworn we had a homework help board but I cannot find it, so yes.

I'm in the middle of an area problem, and I'm stumped. It's a silly question but can anyone tell me the antiderivative/integral of cos^3(t)? Surely it's not (cos^2(t))/3, right?

Wait... woah, trippy, it's 0, isn't it? but how does one realize that without looking at the graph?

Also, okay, the actual question is, "Find the area of the region enclosed by the astroid x=(a)(cos^3(t)), y=(a)(sin^3(t)). ... but is it just 0? can I do that?

confused. I hate calc.

[Hydrogen]

The integral of Integral of cos(t)^3 = (9*Sin[t] + Sin[3*t])/12



Hopefully you can take it from there. Let me know if you need help. I did this stuff last quarter. Also, I didn't compute this integral by hand. I had an online software do it for me. I dont know if I want to give it to you just yet because if you are like me, you will use it too much and won't learn how to actually do the integrals and then be screwed on the test . Let me know if you aren't like that. Then I will give it to you .

[jillian]

*stares at it for a while* Oh. That's complicated.

Yeh, I had a terrible calc teacher last semester for introduction - add that to the fact that I was one of 3 kids in the whole intro class who hadn't had calc before and I was basically screwed. I don't understand any of it. ._. Thank you for your help, but yeah, I do feel silly answering when I don't know how to go about it. I guess I'll go to the teacher... Thanks darling. <3

[Hydrogen]

no problem . And don't think too much of the complexity of that integral. I think you just have to apply one of those tricks that you just have to know for integrals. Integrals are a pain in that way...

And give it your best shot . Learn the basics well now, since later calculus gets much harder. I was actually wrong...I didn't do this stuff last quarter....I did this stuff exactly one year ago . The stuff i did last quarter involved volumes and integrals too...but it was like triple integrals to take the volume of any object in 3 dimensions...



You'll be fine .

[Alex]

The integral of Integral of cos(t)^3 = (9*Sin[t] + Sin[3*t])/12



Hopefully you can take it from there. Let me know if you need help. I did this stuff last quarter. Also, I didn't compute this integral by hand. I had an online software do it for me. I dont know if I want to give it to you just yet because if you are like me, you will use it too much and won't learn how to actually do the integrals and then be screwed on the test . Let me know if you aren't like that. Then I will give it to you .

Did you get that by memory? Or did you look it up. Looks like one of those "Look in the back of the book for formula" instances =p