Compute the lower Riemann sum for the given function f(x)=cos(x) over the interval of [0,pi] with respect to the partition P=[0, pi/3, pi/2, pi]. What I don't understand about this problem is how to compute the sum when xpi/2 its negative.

Question

Compute the lower Riemann sum for the given function f(x)=cos(x) over the interval of [0,pi] with respect to the partition P=[0, pi/3, pi/2, pi]. What I don't understand about this problem is how to compute the sum when x<pi/2 it is positive and when x>pi/2 its negative.

amistre64 · Answer

the lower sum is for the rectangles inside the curve right?

amistre64 · Answer

might have to refresh me on what a "lower" sum is :/

amistre64 · Answer

..using the lower of the endpoints of the interval

amistre64 · Answer

min(cos 0, cos pi/3)
+ min(cos pi/3, cos pi/2)
+ min(cos pi/2, cos pi)

amistre64 · Answer

of course, times the width of each interval