Post # 25

So, when i was actually at school we did things involving taking more practice ap's..



so in attempts to teach this to myself, i'm going to explain trapezoidal rule..



so if i do anything wrong, i would appreciate if someone could just comment it and let me know..or easier tricks to learning it!



so, here it goes..



LRAM is left hand approximation and the formula is:

delta x [f(a) + f( delta x +a) .... + f( delta x - b)]



Say you are asked to calculate the left Riemann Sum for -4x -5 on the interval [-3, -1] divided into 2 subintervals.



delta x would equal: -1+3 /2 = 2/2 =



11[ f(-3) + f(-3 +1)]1[ f( -3) + f(-2)]



then plug into your equationRRAM is right hand approximation and the formula is:



delta x [ f(a + delta x) + .... + f(b)]



so using the same example:



1[ f( -2) + f(-1)]



and then plug into your equation...



MRAM is to calculate the middle and the formula is:



delta x [ f(mid) + f(mid) + .... ]



To find midpoints, you would add the two numbers together then divide by two



In this problem the numbers would be: -3 , -2, -1-3 + -2/ 2

= -5/2 and -2 + -1 / 2

= -3/2

so 1[f(-5/2) + f(-3/2)]



and the plug in..



Trapezoidal is different because instead of multiplying by delta x, you multiply by delta x/2 and you also have on more term then your number of subintervals.



The formula is : delta x/2 [f(a) + 2f(a + delta x) + 2f(a+ 2 delta x) + ....f(b)]



For this problem: 1/2 [ f(-3) + 2 f(-2) + f( -1)] and then plug in.



THat's really the only thing i'm confused about..my silly mistakes ruin my ap scores...