Use calculus to find the area A of the triangle with the given vertices.(0, 0),    (6, 1),    (2, 6)A =

To find the area of a triangle using the coordinates of its vertices, you can use the formula for the area of a triangle in a coordinate plane:

A = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices of the triangle.

In this case, the coordinates are (0, 0), (6, 1), and (2, 6). So, x1 = 0, y1 = 0, x2 = 6, y2 = 1, x3 = 2, and y3 = 6.

Substitute these values into the formula:

A = 1/2 * |0*(1 - 6) + 6*(6 - 0) + 2*(0 - 1)|

Simplify the expression inside the absolute value:

A = 1/2 * |-0 + 36 - 2|

A = 1/2 * |34|

The absolute value of 34 is 34, so:

A = 1/2 * 34

A = 17 square units

So, the area of the triangle is 17 square units.