Question

Calculate the left Riemann sum for the given function over the interval (-2,2) using n=4
f(x)=2*x^2

Calculate the left Riemann for the given function over the interval (0,10) using n=5
f(x)=25*e^-x

Answer 1

for the first one, using the LRS, you're using the left endpoint of each subinterval: x=-2, -1, 0, 1.
the height of the rectangles at each of those left endpoints is f(-2), f(-1), f(0), f(1)
So the LRS approximation with n=4 for f(x)=2x^2 is
LRS = [ f(-2) + f(-1) + f(0) + f(1) ]*1

basically you do the same thing with the second function but the width of each of your subintervals will now be 2...