What is the area of triangle bounded by the x-axis, the y-axis, and the line y=−4x+4?

Question

What is the area of triangle bounded by the x-axis, the y-axis, and the line y=−4x+4?

Answer 1

The area equals to the integral of the function f(x)=-4x+4 from 0 to 1 which is the same as the quantity

[(-2x^2+4x) evaluated at 1] minus [(2x^2+4x) evaluated at 0]=-2+4-(0)=2.