Calculus
posted by Jennifer .
I have two questions, because I'm preparing for a math test on monday.
1. Use the fundamental theorem of calculus to find the derivative:
(d/dt) the integral over [0, cos t] of (3/5(u^2))du
I have a feeling I will be able to find the derivative easily, I'm just having trouble with the very first step finding the integral. The only thought I've had so far is possibly rearranging the function like this:
3(5(u^2))^1
but I don't know if can work like that. Any ideas?
2. Evaluate these trigonometric integrals:
integral of sin(^2)x*cosx(dx)
I think I may have to use a substitution here, but I'm not sure. I started like this:
(sin(x))^2 + (cos(x))^2 = 1
therefore (sin(x))^2=1(cos(x))^2
so:
the integral of (1(cos(x))^2)cosx dx
which brings us to:
integral of cosx(cos(x))^3dx
Now I know I could split that up into two integrals, but we haven't learned the integral of (cos(X))^3. I could make a substitution where u=cosx and du/sinx= dx, but then my integral would be:
integral of (u^3)(cscx)du
which doesn't make the problem any more simple. Any ideas? Was it wrong to make the substitution for (sin(x))^2 at the start?
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