Partial Fraction Deconstruction: Int Tutorial

[suspenc3]

Hi, here is my question:

$$\int \frac{dx}{(x-2)(x^2+4)}$$...for some reason I can't equate the coefficients?..is there something else.i used A/x-2 + B/(x^2+4)

 

[StatusX]

When you have an irreducible quadratic polynomial in the denominator, you have to expand it as follows:

$$\frac{A}{x-2}+\frac{Bx+C}{x^2+4}$$

Now you have as many equations (equating the coefficients of 1, x and x² after multiplying across by the denominator) as unknowns (A,B,C).

 

[suspenc3]

ohhh..ok Thanks!

 

[suspenc3]

I have another question..Im just starting ttrapezoidal rule, are you suppose to use a calculator or?

 

[StatusX]

What are you trying to do? If your goal is to numerically approximate the integral of a function that can't be done analytically, you should use a computer program. If you're just supposed to demonstrate the trapezoidal rule for small numbers of intervals (ie, a few, wide trapezoids), then it depends. Sometimes you can find an exact expression for the sum of their areas, as in the case of the function f(x)=x, and sometimes this may be difficult and you'll just want to add up the areas on your calculator.

 

[Mindscrape]

I've always wondered why they teach the trapezoidal rule anyway. Obviously if you are looking for an approximation to a non-integrable (sp?) function then you will use a better method like Simpson's rule, and for anything that you would be able to use the trapezoidal rule with any close approximation you might as well just use rectangles.

Anyway, I'd imagine that you're supposed to use a calculator to go through the approximations, or if it is one of that calc classes where you aren't allowed to use a calculator then you should just put all your work down and they will grade based on that (so much easier).

 

[suspenc3]

Hi, late response sorry, I am doing pretty complex numbers..I don't think I could do them in my head..like $$(1.6+1)^1^/^4$$ and cosine of a fraction etc...Ive never really used a calculator fot he past 3 years and I don't see why we would all of a sudden need one... Also..is it just me or is the trap and simpson rule pointless and out of place..it just seems too easy...i dddddddunno

 

[Jameson]

If you can compute 2.6^(1/4) in your head then kudos. I'd save time and use a calculator. (Which is what I suspect you're intended to do)