Sunday
November 23, 2014

Homework Help: Calculus

Posted by Jennifer on Saturday, May 9, 2009 at 11:59pm.

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?

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

Maths Calculus Derivative Integral - Urgent Please - Use 2nd Fundamental Theorem...
Math - Use Part 1 of the Fundamental Theorem of Calculus to find the derivative ...
Math - Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = ...
Calculus AB (AP) - Hi, I have a calculus test tomorrow and I understand how to ...
Calculus - "Leave the answer as a definite integral, but indicate how it could ...
Calculus I - Section The fundamental Theorem of Calculus: Use Part I of the ...
Math:Calculus - Use the Fundamental Theorem of Calculus to find the derivative ...
math, calculus 2 - Use part 1 of the Fundamental Theorem of Calculus to find ...
please help me calc. have test tom - d/dx integral from o to x of function cos(2...
Calculus AP need help! - Use Part 1 of the Fundamental Theorem of Calculus to ...

Search
Members