Alright, so this week we took another ap test, and finally b-rob is coming back! yay!! and unfortunately my binder is completely not ready, so i pray we don't have to turn those in anytime soon. So, this blog is going to be on reimann sums.
Integration uses Riemann sums, which is the approximation of area by using rectangles or trapezoids. Integration is just finding the area of something with a curve that you would not normally be able to get.
So there are four different methods of integration, LRAM, RRAM, MRAM, and trapezoidal.
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)]
on thing i could use some touching up on are those questions that are like, "find the normal line to...."
so yeah, that would be my one question for this blog.
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normal lines are just like tangent lines except you do the inverse of the slope!
ReplyDeletetherefore, take the derivative, find the slope, take it's inverse, then plug into point slope form!
For those, you just find the slope of your tangent line and take the negative reciprocal of it and use it for your slope and plug into point slope form
ReplyDeleteNormal line is the same steps as tangent line. The only thing you do different is take the negative reciprocal of the slope. Therefore, you take the derivative to find the slope, then use the negative reciprocal of that to put into point slope form
ReplyDeletenormal lines are like tangent likes except you use the inverse of the slope.
ReplyDeleteTo find the normal line, you take the derivative of the function and plug in x and solve for the slope just like you would do for a tangent line. When you get your slope, take the negative reciprocal of the slope.. so lets say your slope came out to 1/2.. your normal line would be -2. If need be, you plug into point-slope form.
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