fifth reflection

hmm, well i was gonna do my fifth reflection on area of disks, but it is almost the exact same thing as volume, so i decided against it. and i looked through some stuff and decided i am going to do this one on Riemann Sums!!! (particularly the right Riemann Sum because that is my favorite)

The first formula you need to know is x=(b-a)/n [a,b] with n subintervals. You will need to know this because each of the next formulas require that you know what x is.

LRAM- left hand approximation. (this puts the rectangles used to find the area on the left side of the curve) x[f(a)+f(a+x)+...f(b)]
RRAM- right hand approximation. (this puts the rectangles used to find the area on the right side of the curve) x[f(a+x)+...f(b)]
MRAM- approximation from the middle. (this puts the rectangles right on top of the curve, so that the curve goes through the middle of each one) x[f(mid)+f(mid)+...]
Trapezoidal- this does not use squares, instead it uses trapezoids to eliminate most of the empty space inside the curve, and I think this is the most accurate. x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]


alright, they are all basically worked the same, the only difference is the formulas, so I am just going to work an MRAM problem because that is just a good one i came across.

Calculate the right Riemann Sum for q(x)=-x^2-3x on the interval [-2,1] divided into 4 subintervals

so first, you have to find your delta x which you get from using the formula b-a/n and in this specific example, would be 1+2/4, which is 3/4.

Next you just plug into the formula
3/4[f(-1.25)+f(-.5)+f(.25)+f(1)

so then you plug in those values into the formula they gave you to get:
3/4[-(35/16)-1.25-(11/16)-2]

which is then simplified to -147/32

and that is it. for the other ones you just plug into the other formulas to get the answer, but it is worked basically the same way.

yay, i'm finally done all my reflections