Page 180 - Calculus Workbook For Dummies

164 Part IV: Integration and Infinite Series

9. Simplify as in Step 6. Done! Finally! That’s the formula for
approximating the area under
2
5 n 5 5 n 5 2
= !c n i + ! cm n 3 n im f x = x + 3 x from 0 to 5 with n
^ h
n
i 1 i 1
=
rectangles — the more you use, the
=
n
n
5
5
= ! 25 2 i + ! 15 i better your estimate. I bet you can’t
2
n
n
n
=
=
i 1 n i 1 wait to do one of these problems on
125 n 2 75 n your own.
= 3 ! i + 2 i !
n i 1= n i 1=
Check this result by plugging 20 into n to
10. Now replace the sigma sums with the see whether you get the same answer as
expressions for the sums of integers with the 20-rectangle version of this
and squares of integers like you did in problem.
Step 7. 2
475 20 + 600 20 + 125
h
^
^
h
^
^
125 n n + 1 2 ^h n + 1h 75 n n + 1h = 2 . 84 .2
^
= 3 e o + 2 e o 6 20h
n 6 n 2
It checks.
2
2
250 n + 375 n + 125 75 n + 75 n
= +
6 n 2 2 n 2
2
475 n + 600 n + 125
= 2
6 n
9
10
5. Evaluate ! 4. 6. Evaluate !^ - 1 ^h i i + 1h .
2
=
i 1 i = 0
Solve It Solve It