Write the following improper integral as a limit of definite integrals, or as a sum of limits of definite integrals. DO NOT EVALUATE IT.
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Write the following improper integral as a limit of definite integrals, or as a sum of...
(a) Set up the appropriate limit(s) to evaluate the improper integral Do not evaluate the limit(s). = dr. (6) Determine whether the following integrals is proper, improper and convergent, or improper and divergent. Justify your answer. *1 + arctan(1) 10 (c) Evaluate the following integral or determine whether it is convergent.
8. Write down a definite integral (but do not evaluate) that produces the following limit of sums using the definition of definite integral: b) lim 61 k-l 8. Write down a definite integral (but do not evaluate) that produces the following limit of sums using the definition of definite integral: b) lim 61 k-l
a) Set up the appropriate limit(s) to evaluate the improper integral Do not evaluate the limit(s). Ś 4. 12 - 31 dr. (b) Determine whether the following integrals is proper, improper and convergent, or improper and divergent. Justify your answer. x + arctan(a) x + 3 $ (c) Evaluate the following integral or determine whether it is convergent. 1 S Edi X-V
Evaluate the following integrals and note whether they are definite, indefinite or improper. 2
i. Explain why this definite integral is an improper integral. ii. Determine if this improper integral converges or diverges. Be sure to treat the improper integral with appropriate mathematical rigour. Simply treating the improper integral as if it was a proper integral will result in zero marks. Furthermore, make sure you clearly explain/justify each step in your limit analysis working. thanks for your answer, please give a clear writing. (b) Consider the definite integral 2 1 i. Explain why this...
Select the improper integrals in the following list of definite integrals. 6x ln(x)dx 9dz وه ()tanهه πω 4 tan - da e I 3ln(x)da tdt و 7.5 of de 7dt 1 - t2 du 2 + 9 + 6
Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown. Evaluate the integral exactly. Reimann sum Ay m3 definite integral dy - m3 5 m Ay 5 m 5 m Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown. Evaluate the integral exactly. Reimann sum Ay m3 definite integral dy - m3 5 m Ay 5 m 5 m
(1 point) Call an improper definite integral type 1 if it is improper because the interval of integration is infinite. Call it type 2 if it is improper because the function takes on an infinite value within the interval of integration. Classify the type(s) for each of the following improper integrals. ? 1. sec(x) dx 0 ? 2. $x2-3x+6° x2 - 5x + 6 1 ? 3. Loints dx -00 x2 00 ? 4. dx
Rewrite the limit of each Riemann sum as a definite integral (Show Work) Σ(2 + 3ckAXk| On the interval [0,4] melm mesh0 k-1 Rewrite the limit of each Riemann sum as a definite integral (Show Work) Σ(2 + 3ckAXk| On the interval [0,4] melm mesh0 k-1
. (5pont)Thedale integraltegralsovertherduis an improper integ da dy is an improper integral that could be defined as the limit of double integrals over the rectangle [0,t] x [0, t] as t-1. But if we expand the integrand as a geometric series, we can express the integral as the sum of an infinite series. Show that Tl 2. (5 points) Leonhard Euler was able to find the exact sum of the series in the previous problem. In 1736 he proved that...