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

[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?

 

[tiny-tim]

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.

 

[musichael]

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.

 

[musichael]

the answer should be 25.1

 

[musichael]

I can't figure it out.

 

[tiny-tim]

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.

 

[musichael]

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

 

[musichael]

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

 

[tiny-tim]

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

but the bottom is a - bx²