Homework Statement
Integrate √(x2(x+3)) from -3 to 0.
0
∫√(x2(x+3)) dx
-32. The attempt at a solution
Here is what I did:
√(x2(x+3))
= x√(x+3)
Let u=x+3, du=dx, x=u-3
Insert the bounds and change the bounds to: 0 to 3.
x√(x+3)=
(u-3)√(u)
= u3/2-3u1/2
Thus we have:
3
∫(u3/2-3u1/2) du
0...
Homework Statement
Integrate ettdt using integration by parts.2. The attempt at a solution
Seems like a very easy problem; however, I just started learning integration by parts-- didn't understand this.
So the book's method:
u=t...
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Here it says work=force*distance, and force=mass*acceleration.
In a problem they use gravity for acceleration which I guess you can do.
So they have:
F=mass*gravity
So to calculate the...
Homework Statement
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves about the specified axis.
y=x^4, y=0, x=1; about x=2
2. The attempt at a solution
I know how to do the problem, except how to find the radius. Like I know...
Homework Statement
An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) = 100 e^(-0.01t) liters per minute. How much oil leaks out during the first hour?
Homework Equations
r(t) = 100 e^(-0.01t)
The Attempt at a Solution
Eh, I already got the answer, I...
Homework Statement
http://i50.tinypic.com/zxw6qr.png
a>0
a
∫ x√(x^2+a^2)dx (a>0)
02. The attempt at a solution
u=x^2+a^2
du=2xdx
I looked it up online and I saw you needed to use trig.
How do you use trig for this problem?
Note: I have not learned integration by parts, just u-sub.