how do i use the definition of definite integral to compute the integral from a to b of x dx?

Answer 1

Graph y = a and y = b (so the points are (a,a) and (b,b). Connect them with a straight line. Drop another line from each point straight down to the x-axis. You should have a trapezoid. Find its area; that is the definite integral.

Area trapezoid = (1/2)h(b1 + b2) = (1/2)(b-a)(a+b) =
(1/2)(b^2-a^2)