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

• musichael
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.
musichael
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?

Welcome to PF!

Hi musichael! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

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.

I can't figure it out.

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?

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

Try either a trigonometric substitution, or partial fractions.

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

I tried using partial fractions but I can't figure out how to factor the bottom expression

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

## 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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