University:
Whitman College
Course:
MATH-126 | Calculus II
Academic year:

2023
Views:

338

Pages:

1
Author:

aterizareofn

Extra Practice in Riemann Sums The following formulas may be useful: n X n X n(n + 1)(2n + 1) i = 6 i=1 2 i=1 3 i = n(n + 1) 2 !2 1. For each of the following integrals, write the definition using the Riemann sum (and right endpoints), but do not evaluate them: (a) Z 5 sin(3x) dx 2 (b) Z 3√ 1 + x dx 1 (c) Z 2 ex dx 0 2. For each of the following integrals, write the definition using the Riemann sum, and then evaluate them (MUST use the limit of the Riemann sum for credit, and do not re-write them using the properties of the integral): (a) Z 5 x2 dx 2 (b) Z 3 1 − 3x dx 1 (c) Z 5 1 + 2x3 dx 0 3. For each of the following Riemann sums, evaluate the limit by first recognizing it as an appropriate integral: (a) lim n→∞ (b) n→∞ lim n X 3 i=1 n X i=1 n X n s 1+ 3i (Find four different integrals for this one!) n 25i2 2+3· 2 n 2i (c) n→∞ lim sin 3 + n i=1 ! 5 n 2 n 1

Math 126 Extra Practice in Riemann Sums

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