The area of the triangle with the given vertices using calculus.
i) The triangle with the given vertices.
ii) The area of the enclosed region:
The area A of the region bounded by the curves y=f(x), y=g(x) and the lines x=a and x=b is
fx-gx=fx-gx when fx≥g(x)gx-fx when gx≥f(x)
Equation of line passing through two points (a,b) and (c,d) is given by y-bx-a=d-bc-a
The vertices 2, 0, 0,2, (-1,1)
First, find the equations of lines passing through the given vertices.
An equation of the line passing through (2, 0) and (0, 2) is
An equation of the line passing through (2, 0) and (-1,1) is
And the equation of the line passing through (0, 2) and -1,1 is
Now, use these equations to find the area enclosed by the given vertices.
Similar to Excercise 33, therefore,
Integrating this gives,
Plugging the values
i) The triangle enclosed by the given vertices
ii) Area of the shaded region: