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# Final Project Powerpoint

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### Final Project Powerpoint

1. 1. Applications Of Integrals<br />
2. 2. Rectangular Approximation<br />n= number of rectangles<br />F(x₁)= length of rectangle<br />Δx= width of rectangle<br />Note: Δx= (b-a) n<br />Area = [f(x₁) + … + f(xn)] Δx <br />Δx= difference in integral (b-a)<br /> # of squares<br />
3. 3. L-Ram (Over Approximation)<br />Points are on the LEFT-handed side, on the curve<br />Area = [f(x₁) + … + f(xn)] Δx<br />
4. 4. R-Ram (Under Approximation)<br />Points are on the RIGHT-handed side, on the curve<br />Area = [f(x₁) + … + f(xn)] Δx<br />
5. 5. M-Ram (In-Between Approximation)<br />Points are in the MIDDLE of the curve, not on the curve<br />Area = [f(x₁) + … + f(xn)] Δx<br />
6. 6. Calculator Shortcuts<br />LRAM: sum(seq((f(x)Δx,x,a,b-Δx,Δx))<br />RRAM: sum(seq((f(x)Δx,x,a+Δx,b,Δx))<br />MRAM: sum(seq((f(x),Δx,x,a+Δx,b-Δx,Δx))<br />2<br />2<br />equation<br />width<br />variable<br />width<br />beginning<br />end<br />
7. 7. Which RAM Is Most Accurate?<br />Out of LRAM, RRAM, and MRAM, MRAM is the most accurate<br />It uses a combination of both LRAM and RRAM to get an in-between approximation instead of an over or under approximation<br />If you have an area under the x-axis, compensate for the negative area by putting a – in front of the rectangular areas that fall below the x-axis<br />
8. 8. How Is Rectangular Approximation Linked To Area?<br />Rectangular approximation is linked to area because it takes the area of a number of rectangles fitted under a curve to get an approximation to the real area. <br />Using MRAM and a larger number of rectangles, the area you find will become closer to the actual area<br />
9. 9. Area Methods<br />Area of a Triangle: AΔ= 1bh<br />X-axis: A= <br />Y-axis: A=<br />Inverse Method: <br />Switch x’s & y’s<br />Solve for y<br />Integral: <br />Cone Method: A= <br />2<br />
10. 10. Volume Methods<br />Disk Method:<br />X-Axis: <br />Y-Axis: same as the X-Axis, only change the boundaries and equation to terms of y<br />Washer Method:<br />Shell:<br />Useful for y-axis rotation<br />Same thing as:<br />dx/dy<br />