Find the area of the region bounded by the curves y = x^2 , x = y - 2 in the first quadrant. Please help me guys, please

Find the area of the region bounded by the curves y = x^2 , x = y - 2 in the first quadrant. Please help me guys, please

[VIGNESH B S]

You just have to solve both the equations x = x^2 -2 has two solutions. (You can use solve command with var as x).

then use int cmmand to integrate between the curves.

ie:

use desmos graphing calc. to get idea about curves.

integrate(x+2,0,2) - integrate(x^2,0,2) %integrate x+2 from 0 to 2. - integrate x^2 form 0 to 2. gives area bounded.

for integration command -> use this - https://in.mathworks.com/help/matlab/ref/integral.html

Answer 1

[KSSV]

syms x
y1 = x*x;
y2 = x + 2;
% GEt the intersection point of two curves 
xi = solve(y1-y2);
yi(1) = double(subs(y1,xi(1)));
yi(2) = double(subs(y1,xi(2)));
% plot 
fplot(y1)
hold all
fplot(y2)
plot(xi,yi,'or')

% Find the area 
x = double(linspace(xi(1),xi(2),100));
y1 = x.*x;
y2 = x+2;
fill([x x(end:-1:1)],[y1 y2(end:-1:1)],'r')  % show the calculated area 

a = trapz(x,y2)-trapz(x,y1);  % the area 

[Kommepalli Likhith Kumar Reddy]

But I also want the numerical value of the area, i am only getting figure

[KSSV]

Check the full code .... a is the area dear friend.

[Kommepalli Likhith Kumar Reddy]

Find and visualize the divergence of a vector function F yzi xzj xyk. Please answer this bro.. please

Answer 2

[Kesavaraj]

2. To find the area of the region bounded by the curves y2 = x, y=x-2 in the first quadrant.