Mastering Integration: Step-by-Step Methods Explained | Homework Help

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The discussion centers on a request for step-by-step guidance on solving integration problems, with the user expressing confusion despite knowing the basics. Various integration methods are mentioned, including the power rule, logarithmic rule, exponential rule, trigonometric rule, and inverse trigonometric rule. The user is unsure about how to apply these methods effectively and is seeking clarification on the questions presented. There is a suggestion that the questions may not be strictly divided into parts, implying that the best method should be chosen based on the user's understanding of the integral. Overall, the thread highlights the need for clear explanations and structured approaches to mastering integration techniques.
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Homework Statement



Please view the images, i am quite confused(although i know basics). I would very much appreciate an explanation as to how to solve these problems. The step by step approach.

Again, i would appreciate any response explaining how to do this.

Homework Equations



For part A, the options are...
1. Power rule
2. logarithym rule
3. Exponential rule
4. Trig rule
5. Inverse trig rule

The Attempt at a Solution

 

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clurt said:

Homework Statement



Please view the images, i am quite confused(although i know basics). I would very much appreciate an explanation as to how to solve these problems. The step by step approach.

Again, i would appreciate any response explaining how to do this.

Homework Equations



For part A, the options are...
1. Power rule
2. logarithym rule
3. Exponential rule
4. Trig rule
5. Inverse trig rule

The Attempt at a Solution


Seems to me Exponential Expansion'd be better.. But what kind of question is this, anyways?
 
clurt said:

Homework Statement



Please view the images, i am quite confused(although i know basics). I would very much appreciate an explanation as to how to solve these problems. The step by step approach.

Again, i would appreciate any response explaining how to do this.

Homework Equations



For part A, the options are...
1. Power rule
2. logarithym rule
3. Exponential rule
4. Trig rule
5. Inverse trig rule

The Attempt at a Solution

What have you tried?

Where are you stuck?

You must show an attempt before we can help you. -- See the rules.
 
im stuck everywhere and i have tried, can't produce anything
 
clurt said:

Homework Statement



Please view the images, i am quite confused(although i know basics). I would very much appreciate an explanation as to how to solve these problems. The step by step approach.

Again, i would appreciate any response explaining how to do this.

Homework Equations



For part A, the options are...
1. Power rule
2. logarithym rule
3. Exponential rule
4. Trig rule
5. Inverse trig rule

The Attempt at a Solution


I don't think the questions are in parts, as such. I think you're supposed to choose the best option between those "parts" - i.e. if you think you can the integral directly, then choose the first option. If you think you should sub, choose the second, etc.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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