bmwman
Jan 29, 2009, 02:49 PM
Having difficulty integrating. What will be the derivative and answer. See attachment
16069
galactus
Jan 30, 2009, 11:18 AM
Are you familiar with integration at all? Since this is a fluid force problem, I assumed
perhaps you were in a calculus II class. That is where this stuff is commonly covered.
I assumed wrong?
Anyway, bring the 2 out and rewrite as:
124.8\int_{0}^{1}x\sqrt{1-x^{2}}dx
Now, do you know trig sub? I reckon not?
Use the substitution x=sin(t), \;\ dx=cos(t)dt
By doing this, it changes the limits of integration from x=0.. 1 to 0.. Pi/2
124.8\int_{0}^{\frac{\pi}{2}}sin(t)\sqrt{1-sin^{2}(t)}cos(t)dt
As you hopefully know, cos^{2}(t)=1-sin^{2}(t)
Then, we get 124.8\int_{0}^{\frac{\pi}{2}}sin(t)cos^{2}(t)dt
We can use the identity sin(t)cos^{2}(t)=\frac{sin(3t)}{4}+\frac{sin(t)}{4 }
Now, these are straight forward and we can integrate each separately and finish. Can you do that?