Let F(x) = -x^2+12x. Let W represent the integral \(\int_0^6 \! F(x) \, \mathrm{d}x.\)
Please evaluate W from the part above as a limit of Riemann Sums.
I've been searching for help on this but I cannot find what I am looking for.
+138 Hey there :) I'm not 100% sure what your lesson or teacher is wanting, whether it be a visible graph or just using a calculator, but the limit of the integral from 0 to 6, of F(x), can be modelled by this graph below, If using a calculator, you could simply enter the integral of the equation and let it do the work for you, resulting in an answer of 144 :)
+129849 Very nice, Space Tsunami !!!!
It appears that Space Tsunmai is using the midpoint rule for the height of the rectangles and the width of a single rectangle is .2
If we use this approach we have the area as
.2 [ F(.1) + F(.3) + F(.5) + F(.7) + F(.9) + F(1.1) + F(1.3) + F(1.5) + F(1.7) + F(1.9) +F(2.1) +
F(2.3) + F (2.5) + F(2.7) + F(2.9) + F(3.1) + F(3.3) + F ( 3.5) + F(3.7) + F(3.9) + F(4.1) +
F(4.3) + F(4.5) + F(4.7) + F(4.9) + F(5.1) + F(5.3) + F(5.5) + F(5.7) + F(5.9) ] =
.2 [ 1.19 + 3.51 + 5.75 + 7.91 + 9.99 + 11.99 + 13.91 + 15.75 + 17.51 + 19.19 + 20.79 +
22.21 + 23.75 + 25.11 + 26.39 + 27.59 + 28.71 + 29.75 + 30.71 + 31.59 + 32.39 + 33.11 +
33.75 + 34.31 + 34.79 + 35.19 + 35.51 + 35.75 + 35.91 + 35.99 ] =
.2 [ 127.49 + 311.31 + 281.2 ] ≈
144
