Thread: Integral Test and Estimation Problem Help

Let f be a continuous, positive, decreasing function on [3, ∞). Compare the values of the integral of: A: the integral (from 3 to 10) of f(z)dz, B: summation (sigma notation) of f(n) from 3 to 9, and C: summation (sigma notation) of f(n) from 4 to 10. Answer choices: 1. B>C>A 2. C < A < B 3. A < B < C 4. B < A < C 5. A > B > C 6. B < C < A

I initially picked 5 and was wrong.

How would I do this? I tried drawing rectangles and am still not quite sure what the order of the bigger value is.
Help and feedback appreciated.

Thanks

Well I resolved this problem by using the visual method of drawing rectangles and concluded that the answer is 2, which is C<A<B. Can anyone confirm if this is correct? I need to make sure it is right before I submit my answer.