- #1
Natasha1
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Could anyone explain to me ultra simply by means of a mechanical approach maybe why the integration of 1/(3-0.2x)dx = -5 ln l 3-0.2x l ? thanks
Simple integration problem help
- Thread starter Natasha1
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In summary, to find the integration of 1/(3-0.2x)dx, you first set y = 3-0.2x and then find dy in terms of dx. After doing the calculations, the -5 appears as part of the integration process. To integrate, you substitute the value of dy into the equation and then perform the integration.
- #2
quasar987
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set y = 3-0.2x
- #3
Natasha1
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quasar987 said:
What I don't get is the -5 before the ln l 3-0.2x l ?? :-(
- #4
quasar987
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After you've set y = 3-0.2x, you also have to find dy in terms of dx. Do the calculations and you'll see where the -5 pops in.
- #5
Natasha1
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quasar987 said:
dy = -0.2 and then ?
- #6
xman
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right soNatasha1 said:
[tex] -\frac{1}{0.2} dy =dx\Rightarrow -\frac{1}{2/10} dy = dx \Rightarrow - \frac{10}{2} dy =dx \Rightarrow -5dy=dx [/tex]
now substitute back into equation and integrate
- #7
Natasha1
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xman said:
thanksFAQ: Simple integration problem help
What is a simple integration problem?
A simple integration problem is a mathematical exercise that involves finding the antiderivative (or indefinite integral) of a given function. In other words, it is the reverse process of differentiation, where the goal is to find the original function when given its derivative.
How do you solve a simple integration problem?
To solve a simple integration problem, you need to use integration techniques such as substitution, integration by parts, or trigonometric substitution. These techniques involve manipulating the given function in a certain way to make it easier to integrate.
What are some common integration rules?
Some common integration rules include the power rule, where you add 1 to the exponent and divide by the new exponent, and the constant multiple rule, where you can pull out a constant from the integral. Other rules include the product rule and the quotient rule for integration.
What is the difference between definite and indefinite integration?
Definite integration involves finding the area under a curve between two specific points, whereas indefinite integration involves finding the antiderivative of a function without any specific interval. In other words, definite integration gives a numerical value, while indefinite integration gives a function.
Can you use a calculator to solve simple integration problems?
Yes, most scientific calculators have an integration function that can solve simple integration problems. However, it is important to understand the concepts and techniques behind integration in order to use a calculator effectively and check for any errors in the final answer.