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Calculating Areas and Volumes of Regions Bounded by Curves, Lab Reports of Mathematics

Solutions to calculating the areas and volumes of regions bounded by curves using matlab. It includes examples of finding the area between two curves y=x^2-2x and y=x, y^2=x and y=x-2, and x=y^2 and x=y^3. It also covers the volume of a solid generated by revolving the region bounded by the curve y=(4/(x^2+4)) and the x-axis around the x-axis.

What you will learn

  • How to find the area bounded by two curves y=f(x) and y=g(x) using MATLAB?
  • What is the formula for finding the volume of a solid of revolution?
  • How to calculate the area of the region bounded by the curves x=y^3 and x=y^2 using MATLAB?

Typology: Lab Reports

2020/2021

Uploaded on 03/21/2022

scarletboo
scarletboo 🇮🇳

5 documents

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EXPERIMENT 2-A
1. Find the area of the region bounded by the curve y=x2-2x and the line y=x.
Solution:
clear
clc
syms x
f(x)=x^2-2*x;
g(x)=x;
I = [0,3];
a=I (1); b=I (2);
A=int(f(x)-g(x), a, b);
disp ('Area bounded by the curves f(x) and g(x) is:' );
disp(A);
fplot(f(x), [a, b]); grid on; hold on;
fplot(g(x), [a, b]); hold off
xlabel('x-axis'); ylabel('y-axis');
legend('y=f(x)','y=g(x)');
Output:
2. To find the area of the region bounded by the curves y2=x, y=x-2 in the first quadrant.
Solution:
clc
syms x
f(x)=x^1/2;
g(x)=x-2;
I= [1,4];
a=I (1); b=I (2);
A=int(f(x)-g(x), a, b);
pf3
pf4

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EXPERIMENT 2-A

1. Find the area of the region bounded by the curve y=x^2 -2x and the line y=x. Solution: clear clc syms x f(x)=x^2-2*x; g(x)=x; I = [0,3]; a=I (1); b=I (2); A=int(f(x)-g(x), a, b); disp ('Area bounded by the curves f(x) and g(x) is:' ); disp(A); fplot(f(x), [a, b]); grid on; hold on; fplot(g(x), [a, b]); hold off xlabel('x-axis'); ylabel('y-axis'); legend('y=f(x)','y=g(x)'); _Output:

  1. To find the area of the region bounded by the curves y_^2 =x, y=x-2 in the first quadrant. Solution: clc syms x f(x)=x^1/2; g(x)=x-2; I= [1,4]; a=I (1); b=I (2); A=int(f(x)-g(x), a, b);

disp ('Area bounded by the curves f(x) and g(x) is:'); disp(A); fplot(f(x), [a, b]); grid on; hold on; fplot(g(x), [a, b]); hold off xlabel('x-axis'); ylabel('y-axis'); legend('y=f(x)','y=g(x)'); Output:

3. Find the area of the region bounded by the curves x=y^3 and x=y^2_. Solution:_ clc syms x y f(x)=y^3; g(x)=y^2; I= [0,1]; a=I (1); b=I (2); A=int(f(x)-g(x), a, b); Disp ('Area bounded by the curves f(x) and g(x) is:'); disp(A); fplot(f(x), [a, b]); grid on; hold on; fplot(g(x), [a, b]); hold off xlabel('x-axis'); ylabel('y-axis'); legend('y=f(x)','y=g(x)'); Output:

zlabel('Z-axis'); Output: