How do I use the trapezoidal rule to approximate the area bound by y= sin^2x, x=0, y=0, and x=1?
Help appreciated! ^-^

Question

How do I use the trapezoidal rule to approximate the area bound by y= sin^2x, x=0, y=0, and x=1?
Help appreciated! ^-^

anonymous · Answer

oh and I'm supposed to use n= 4
so I am thinking the integral is from 0 to 1 right? 
so since I need 4 segments, should I use .25, .5, .75, and 1?
I tried the problem once this way and got .316 but I am pretty sure this is incorrect. Anyways, I'm stuck, so I would love some help!

anonymous · Answer

The trapezoidal rule is that the area at every segment from a to b can be approximated by $Y(a, b) = (b-a)\frac{f(a) + f(b)}{2}$ (nonstandard symbol $Y$). In your case, the approximation becomes $Y = Y(0, .25) + Y(.25, .5) + Y(.5 + .75) + Y(.75, 1)$. Because $(b-a)$ is constant throughout all four terms, the expression can be simplified using the identity $a(b+c)=ab+ac$: $Y = \frac{b - a}{2}\left(\frac{f(0)}{2}) + f(.25) + f(.5) + f(.75) + \frac{f(1)}{2}\right)$ where $b - a = .25$.

anonymous · Answer

i got 0.27743

anonymous · Answer

lets see what i get

anonymous · Answer

thank you for your replies! I'll just take a minute to look them over and then see if I made any mistakes.

anonymous · Answer

|dw:1398497702737:dw|