Trapezoidal Rule for int [tan x^2] dx from 0 to sqrt[pi/4]

[lucidbabble]

Hi, can anyone please tell me how to set up a problem using the Trapezoidal Rule?

int [tan x^2] dx from 0 to (pi/4)^1/2 , n=4

Is this method similar to that of finding the exact value of a definite integral? I see the formula in my book, but I don't know what to plug in.

All I know is (b-a)/2n = (pi/4)^(1/2).

What do I do from there? How many terms am I supposed to add together? Also, what is the rule about the coefficients? Why do they follow the pattern of 1, 2, 2, 2?

Thanks in advance!

 

[tkhunny]

You cannot be require to do such a thing without an introduction to the topic. Something is out of order as the question stands.

A trapezoid is just a trapezoid. The "Trapezoidal Rule" is an approximation technique (exact under specific circumstances) for a definite integral. You draw as many trapezoids as you like, (n-4 in this case), and you calcualte their areas.

Now hit those books and get some background before you are required to do other things for which you are not prepared.

 

[galactus]

As the name implies, the trapezoid rule adds up the area of the trapezoids under the curve. Any calc book, the internet, etc can be used as a source on the topic.

Here's a diagram to get you started:

EDIT: Sorry, looks like I used \(\displaystyle (\frac{{\pi}}{4})^{2}\) instead of \(\displaystyle \sqrt{\frac{\pi}{4}}\) as the upper limit of integration.

 

[lucidbabble]

Hmm, for some reason, I can't see the image.

Thanks for your help. I did read the book, I just wasn't sure what it meant and how to put the formula to use because I wasn't in class that particular day. Sorry if it seemed like I was lazy - I honestly didn't understand it.