- #1
nameVoid
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Mastering the Definite Integral: A Comprehensive Guide
- Thread starter nameVoid
- Start date
In summary, the conversation is about finding an anti-derivative that will result in (x-2)^1/2 when differentiated. The suggestion is to use substitution with u = x-2.
- #2
CompuChip
Science Advisor
Homework Helper
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Welcome to PF nameVoid.
Let's start by finding an anti-derivative (primitive)... you need something which will give you
[tex]\sqrt{x - 2} = (x - 2)^{1/2}[/tex]
when you differentiate it... can you make a wild guess?
Let's start by finding an anti-derivative (primitive)... you need something which will give you
[tex]\sqrt{x - 2} = (x - 2)^{1/2}[/tex]
when you differentiate it... can you make a wild guess?
- #3
nameVoid
- 241
- 0
using the definition
im not clear on how to expand the expression to distribute the sum
im not clear on how to expand the expression to distribute the sum
- #4
Mark44
Mentor
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Look at CompuChip's post again. He's not asking you to use the definition of the definite integral, but rather asking you if you can think of a function whose derivative is sqrt(x - 2).
IOW, d/dx(____) = (x - 2)^(1/2).
Can you fill in the blank?
IOW, d/dx(____) = (x - 2)^(1/2).
Can you fill in the blank?
- #5
NoMoreExams
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Why don't you just do a subst. u = x - 2?
1. What is a definite integral?
A definite integral is a mathematical concept used to calculate the exact area under a curve on a graph. It is represented by the symbol ∫ and has a lower and upper limit of integration.
2. Why is mastering the definite integral important?
Mastering the definite integral is important because it is a fundamental skill in calculus and is used in many real-world applications, such as calculating displacement, velocity, and acceleration, as well as finding the area and volume of irregular shapes.
3. What are the steps for solving a definite integral?
The steps for solving a definite integral are:1. Identify the function and limits of integration2. Simplify the integrand if possible3. Use integration rules or techniques to solve the integral4. Evaluate the integral using the limits of integration
4. What are the different integration techniques?
The different integration techniques include:1. Power rule2. Substitution method3. Integration by parts4. Partial fractions5. Trigonometric substitution6. Tabular integration7. Improper integration
5. How can I practice and improve my skills in mastering the definite integral?
You can practice and improve your skills in mastering the definite integral by solving a variety of integration problems, using online resources and practice exercises, studying and understanding integration techniques, and seeking help from a tutor or teacher if needed.
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