Question

How do you evaluate the definite integral by the limit definition given `int (1-absx)dx` from [-1,1]?

Answer 1

`int_(-1)^(-1) \ 1-|x| \ dx = 1`

Explanation:

This is a graph of the function:
graph{1-|x| [-2.52, 2.48, -0.91, 1.59]}

As a define integral represents the area under the graph of the function, then simply be elementary geometry, the area is two triangles (or a square); hence without any calculation;

`int_(-1)^(-1) \ 1-|x| \ dx = 1`

I will leave it to someone else to evaluate using the limit definition, but essentially it will be a limit derivation of the area of a triangle.