Oh. I was taught that I could do ½ln|x + ½ + √[(x+½)2-¾]| - ln√(¾) so that C1 = ln√(¾) + C. Is that wrong? Oh, and it's also the first term that I"m having denominator troubles with. The tanθ! I believe I did add the secθ and tanθ with common denominators within the ln expression, as you said.
Homework Statement
So, I have a trigonometric substitution integration problem. The working is rather hairy, but I've gotten to the point where you draw the triangle to express theta in terms of x. But that's where I'm stuck! I think I may be having trouble with the constant of integration...
Homework Statement
The antiderivative of (e^sin(t)) *(cos(t)) is e^(sin(t)) + C? Why is this? What happened to the cos(t)? Is there the chain rule or something applied? I don't know! It just looked like it disappeared.
OH I
Sorry I posted replies that I didn't mean to I'm new to this forum and there are a lot of brackets saying quotes and stuff and it confuses me and I'm not sure what I"m inputting when I hit post reply. Sorry. Thanks for the help A LOT! I did double check everything.
Oh. Wouldn't subtracting the functions from x=3 give the distance from it and thus the radii desired? Then subtracting the inner function from the outer function should give the area I want to integrate, right? That gives me ∫ pi[5y-(2/3)y^3], doesn't it?
But the textbook says (10)(sqrt2)(pi)/3.
Homework Statement
Find volume when the area rotates around a line.
Homework Equations
x=y^2
x=1-y^2
about x = 3
The Attempt at a Solution
Could someone please check my formula for Area? I have pi[ (3-(y^2))^2 - (2-(y^2))^2 ] which gives me the integral pi[5y-(2/3)y^3]. I think...
Homework Statement
How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified lines?
I keep getting a negative number and I"m becoming so frustrated! 11pi/30 is the answer in the textbook. Thank you so very much in advance...