Lab1 Ana Barcari - maple lab PDF

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> Name:Ana Barcari Course: Calculus II Maple Lab Prof.: Dr. Lawrence Assignment:#1 Date: 06/14/2020 > > > (1) > > Part A: Question: A. f(x) = x^2 - x x = 0, x = 2 1. Find the exact area of the given region 2. Find the approximate value of the area using Riemann Sum(right-hand method) for the following partitions: i. n=10 ii. n= 100 iii. n= 1000 3. What happens as n increases? 4. What happens when n goes to infinity >

> (2) USING THE RIGHT-HAND METHOD:

> > (3) > b) Find the approximate value of the area using the different partitions: 1. For n =10 > (4) > (5)

(5) > (6) > (7) > (8) > 0.8800000000

(9)

0.6868000000

(10)

0.6686680000

(11)

> c) Using right-hand method and n =100 > > d) Using right-hand method and n =1000 > > e) > (12) > Conclusion1: As n increases, the approximate value decreases towards the exact value Conclusion2: We see that as n approaches infinity, the Reimann Sum yields the exact value of the area. n=10:Graph: > (13) > (14) > 0.6666666667 > with(Student[Calculus1]): > f:=x->x^2-x; (15)

> Int(f(x), x=0..2); (16) > evalf(%); 0.6666666667 > ApproximateInt(f(x), x=0..Pi/2, method=random, partition=10, output=plot);

> ApproximateInt(f(x), x=0..Pi/2, method=lower, partition=10, output=plot);

(17)

> Part B: B. g(x) = x^3 x = -1 , x = 0 1. Find the exact area of the given region 2. Find the approximate value of the area using Riemann Sum(left-hand method) for the following partitions: i. n= 10 ii. n= 100 iii. n= 1000 3. What happens as n increases? 4. What happens when n goes to infinity > (18) >

> (19) > (20) b) Find the approximate value of the area using the different partitions: 1. For n =10 > (21) > (22) > (23) > (24)

USING THE LEFT-HAND METHOD: > > (25) > > (26) > (27) > c) Using left-hand method and n =100 > (28) > d) Using left-hand method and n =1000 > (29) > e) > (30) > Conclusion1: As n increases, the approximate value increases also towards the exact value Conclusion2: We see that as n approaches infinity, the Reimann Sum yields the exact value of the area. > g:=x->x^3; (31) > Int(g(x), x=-1..0); (32) > ApproximateInt(g(x), x=-1..0, method=upper, partition=10, output= plot);

> ApproximateInt(g(x), x=-1..0, method=random, partition=20, output=plot);...