# Integrating square roots with trig function and constant inside

## Homework Statement

∫√(2+cos3(t)) dt

I should perhaps have tried to get the lower and upper limits of this integral (it's defined), but all I'm wondering about is how to calculate the integral. I don't need the answer, but if someone could just point me in the right direction. I've tried "normal" substitution, but I can't find a smart u :P

I appreciate any hints :D

PS! I'm Norwegian, and so my mathematical formulations might be slightly off, I'm used to write this stuff in Norwegian, haha:)

Char. Limit
Gold Member
I don't think this integral has a closed-form solution. You'll have to try numerical integration.

I don't think this integral has a closed-form solution. You'll have to try numerical integration.

I'm sorry, I forgot to add something crucial into the first post. The whole task is:

y=∫√(2+cos3(t)) dt
upper limit: 7x2
lower limit: 2

find dy/dx

Now, I do not think I can use Calculus's fundamental theorem, and just say that if y=F(x) then F'(x)=y. The function isn't really defined on a closed interval, "7x2" isn't a defined upper limit, right?

I'm not sure here, what do you think?

Last edited:
Char. Limit
Gold Member
Hehe, the function is in no way constant.

Hmm... I prefer Simpson's Method for high accuracy. But use whichever you want; it sounds like you already know how to numerically integrate.

I wasn't aware of any Simpson's method. I'm in Calculus 1, the first course in my first year at uni. I'm not really good - yet:) The main difference so far from high school is arguing to prove a certain rule, the differential rules, for example. I just don't need to know how to use them, I must understand them as well. And the formulations are very new for me. Anyway, I can't use numerical integration as I must find the function y, and not the area under the graph.