Integrating from 0 to 200 of 1/(14-(.0003x^2))

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In summary, the conversation involves someone seeking help with an integral problem. They tried using a logarithmic function and partial fractions but were unable to get the correct answer. The function being integrated is 1/(14-.0003X^2) and the suggestion is to try a trigonometric substitution or partial fractions.
  • #1
musichael
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I can't figure out how to this integral. I keep coming up with the wrong answer. Can someone please show me a detailed solution?
 
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  • #2
Welcome to PF!

Hi musichael! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 
  • #3
ok first i did ln(14-.0003x^2) divided by the derivative of the inside. but when i plug in the definate integral values i can't get the correct answer.
 
  • #4
the answer should be 25.1
 
  • #5
I can't figure it out.
 
  • #6
musichael said:
ok first i did ln(14-.0003x^2) divided by the derivative of the inside. but when i plug in the definate integral values i can't get the correct answer.

uhh? :confused:

d/dx(ln(14-.0003x^2)) = (.006 x)/ln(14-.0003x^2).

Try either a trigonometric substitution, or partial fractions. :wink:
 
  • #7
the function that i need to integrate is 1/(14-.0003X^2) I am pretty sure you use the Ln(14-.0003X^2)/(2(.0003x) but It doesn't work with 0 to 200
 
  • #8
I tried using partial fractions but I can't figure out how to factor the bottom expression
 
  • #9
musichael said:
I tried using partial fractions but I can't figure out how to factor the bottom expression

but the bottom is a - bx2 :frown:
 

Related to Integrating from 0 to 200 of 1/(14-(.0003x^2))

1. What does it mean to integrate from 0 to 200?

Integrating from 0 to 200 means finding the area under the curve of a given function from x=0 to x=200.

2. What is the significance of 1/(14-(.0003x^2)) in this integration?

The function 1/(14-(.0003x^2)) represents the height of the curve at any given x-value. It is the integrand that is being integrated to find the area under the curve.

3. How is the integration from 0 to 200 different from other types of integrations?

The limits of integration, in this case 0 and 200, determine the range of x-values for which the area under the curve is being calculated. Other integrations may have different limits that correspond to different ranges of x-values.

4. Is there a specific method for integrating from 0 to 200?

Yes, there are various methods for integrating from 0 to 200, such as the midpoint rule, trapezoidal rule, and Simpson's rule. The choice of method depends on the complexity of the function and the desired level of accuracy.

5. What does the result of this integration represent?

The result of this integration represents the total area under the curve of the given function from x=0 to x=200. In other words, it gives the value of the definite integral of the function over the given interval.

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