Calculus  Integrals
posted by Sean .
I know I've probably flooded the site or something (Sorry if I have), it's just that these problems aren't similar to anything I've reviewed in class. I've got two more questions, then maybe 1 or 2 more coming. That's all I can see in the future, anyhow.
1) Integral of [2* sqrt((1+cosx)/2)].
All I can see is that I take the 2 out of the integral, and put it out front.
2) Integral of [(sec(x))^4].
Here I'm completely stumped. I'm not sure how to start, either.
I'd really appreciate help on these two problems. They've really got me stuck.
P.S. Also, if anyone could supply a link of math tutorials of some sort, please do!

1) use the formula:
cos(2x) = 2 cos^2(x)  1
You can use this formula to derive a formula for cos(1/2 x) in terms of
cos(x). You can then simplify the square root using that formula.
2) sec^4 (x) = 1/cos^4(x)
You can use a reduction formula, which is easier to derive for positive powers of cos,, you just apply that backwards for this case.
Notation cos = c, sin = s:
c^n = c^(n2)c^2 = c^(n2)[1s^2] =
c^(n2)  c^(n2)s^2
So the integral of c^n is the integral of c^(n2) minus the integral of
c^(n2)s^2. This latter integral can be written up to a minus sign:
Int of c^(n2)sdc = ( let's do a partial integration) =
Integral of s d[c^(n1)/(n1)] =
Integral of d[sc^(n1)/(n1)] 
Integral of c^(n1)/(n1)ds =
sc^(n1)/(n1) 
Integral of c^(n)/(n1) dx
So, we have expressed the integral of cos^n in terms of the integral of
cos^(n2), a trignometric function and cos^n again. You can bring that later integral of cos^n back to the other side of this expression and solve for the integral of cos^n in terms of the integral of cos^(n2).
You can then verify that this equation is also valid for negative n (that's is trivial). So, you can use it to express the integral of 1/c^4 in terms of the integral of 1/c^2, that latter integral is of course, the tan function. 
I don't quite get how you did the first one. Mainly the cos(1/2 x)
Respond to this Question
Similar Questions

eng 34
i need the chapter reveiw questions for the story Two Friends in english 34 please Sorry  but we don't have copies of textbooks. You can probably get the questions from a classmate. 
Homework
We, my roomates and I, keep getting replies saying stop posting under more than one name. We are not posting under more than one name we are all different. We all live together and only have this common computer at the moment, but … 
Math
How do I multiply more than two binomials? 
calculus help
Is there any good calculus websites out there that teach every possible derivative there is? 
Calculus
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 … 
English
1. They want to have more of something such as food or money than is necessary or fair. (What is the positive degree of 'more'? 
algebra...
In a school, there are 4 more students in Class A than in Class B, and 4 more students in Class B than in Class C. As a reward for good behavior, a teacher decides to give out some sweets. Every student in class C got 5 more sweets … 
Tan^2 Integrals
I'm having a hard time understanding how to do Integrals involving tan^2. I have two problems: 1. Find the integral of (tan^2 y +1)dy 2. Find the integral of (7tan^2 u +15)du 1. My approach to it is to replace the tan^2 y portion of … 
math analysis
((x+3)/(x5))+(5/(x3)) Simplify I've done this twice and got it wrong both times I have two more problems similar to this and don't want to continue until I understand how to do it. 
Math
6 cd+2b+9(cd+b/3)=A(3cd+b) I'm really sorry this question seems really hard to me. But what I got as an answer is 6, ohh and I have another question. Can you use the distributive property on this problem?