Approximating the integral from 0 to 6 of (e^x dx) by 3 circumscribed rectangles of equal width on the x-axis yields ____.

Question

a) 2e^2 + 4e^4 + 6e^6
b) 2(e^2 + e^4 + e^6)
c) 2(e + e^3 + e^5)
d) e + 3e^3 + 5e^5
e) e^2 + 3e^4 + 5e^6

Answer 1

sketch the graph of e^x with the rectangles of height e^2, e^4 and e^6 and base of 2 each
2 e^2 + 2 e^4 + 2 e^6

= 2 (e^2 + e^4 + e^6)

Answer 2

Not sure what the "circumscribed" condition means, since any rectangle can be circumscribed.

Damon's rectangles contain the approximated sections of curve within them, whatever that means.

However, since the other choice of boundaries yields 2(1+e^2+e^4), its absence from the list leaves us no other, uh, choice.

Answer 3

I assumed circumscribed meant outside, but it is unclear indeed.