Integrating square roots with trig function and constant inside

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Homework Help Overview

The discussion revolves around the integral ∫√(2+cos3(t)) dt, with a specific focus on its evaluation and the implications of its limits, which are defined as upper limit: 7x² and lower limit: 2. The original poster expresses uncertainty about how to approach the integral and whether it has a closed-form solution.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the possibility of using substitution methods and numerical integration. The original poster questions the applicability of the fundamental theorem of calculus due to the nature of the upper limit. There is also mention of the need to understand the underlying concepts rather than just applying rules.

Discussion Status

The discussion is ongoing, with participants exploring different methods of integration and questioning the nature of the integral's limits. Some guidance has been offered regarding numerical integration, but there is no consensus on the best approach or the existence of a closed-form solution.

Contextual Notes

The original poster notes that they are in their first year of university calculus and are still becoming familiar with mathematical formulations and concepts. There is an acknowledgment of potential language barriers in expressing mathematical ideas.

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Homework Statement



∫√(2+cos3(t)) dtI 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:)
 
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I don't think this integral has a closed-form solution. You'll have to try numerical integration.
 
Char. Limit said:
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:
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.
 

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