Is Mid(n) an Underestimate for Trapezoid Integration on an Increasing Function?

[chjopl]

For F(x) dx from a to b show TRAP(n)=Left(n) + 1/2 (f(b)-f(a))*delta x

 

[HallsofIvy]

I assume that TRAP(n) is the value you would get using n trapezoids to approximate the area. Is Left(n) the approximation using rectangles with height the left endpoint?

If so, you might note that TRAP(n)= (Left(n)+ Right(n))/2 and that the sums involved in Left(n) and Right(n) differ only at the two endpoints.

 

[chjopl]

Thanks for the help but now i have another problem
Let f''> 0 and suppose f is increasing on [a,b], show that Mid(n) is an underestimate for f(x) dx from a to b.