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Problem 3 Integrate: tan-1 12 dc 1 + x2 Hint: This integral is improper! Begin by...
Problem 3 Integrate: tan-12 du 1 + x2 Hint: This integral is improper! Begin by writing...
Problem 3 Integrate: tan-12 du 1 + x2 Hint: This integral is improper! Begin by writing the improper integral as the appropriate limit. Then ask yourself: what is the derivative of tan-1x? (Show all details.) st
Question 2 please 1 and 2, determine whether or not the integral is In exercises improper. If it is improper, explain why 12. (a) 12 x-2/5 dx 「x-2/5 dx 「x2/5 dx (b) (c) I. (a) 0 13. (a 40 1 dx 2 x...
Question 2 please
1 and 2, determine whether or not the integral is In exercises improper. If it is improper, explain why 12. (a) 12 x-2/5 dx 「x-2/5 dx 「x2/5 dx (b) (c) I. (a) 0 13. (a 40 1 dx 2 x 14. (a In exercises 3-18, determine whether the integral converges or diverges. Find the value of the integral if it converges. 15. (a (b)人1x-4/3 dr 3, (a) l.lyMdx (b) x43 dx 16. (a 4. (a) 45 dx...
. (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...
. (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...
Use trig identities to rewrite the integral then integrate. 1. 2. 3. 4. 5. 6. tan(r)dr tan(r)dr (sinz + sinz +...
Use trig identities to rewrite the integral then integrate. 1. 2. 3. 4. 5. 6. tan(r)dr tan(r)dr (sinz + sinz + tan2)/sec2rda Sin.TS2nT (sin(2x)/cosrdr (sin(2))/1+cos2rda (cos(x) + sin(2))/sinrdr tan(r)dr tan(r)dr (sinz + sinz + tan2)/sec2rda Sin.TS2nT (sin(2x)/cosrdr (sin(2))/1+cos2rda (cos(x) + sin(2))/sinrdr
tan-i (-1+-- 2. Express the limit lini Σ 2n 2 as a definite n 2n integral. Make sure to fully justify your work. Hint:...
tan-i (-1+-- 2. Express the limit lini Σ 2n 2 as a definite n 2n integral. Make sure to fully justify your work. Hint: What is equal to?
tan-i (-1+-- 2. Express the limit lini Σ 2n 2 as a definite n 2n integral. Make sure to fully justify your work. Hint: What is equal to?
Q9 (Approximation of π) (a) Show that 1/1 + t2 = 1 − t2 + t4 − ... + (−1)n−1 t 2n−2 + (−1)n t2n /1 + t2 for all t ∈ R and n ∈ N. (b) Integrate both side in (a), show that tan−1 (x) = x − x3/3 + x5 /5...
Q9 (Approximation of π) (a)
Show that 1/1 + t2 = 1 − t2 + t4 −
... + (−1)n−1 t 2n−2 + (−1)n
t2n /1 + t2 for all t ∈ R and n ∈ N.
(b) Integrate both side in (a), show that tan−1 (x) =
x − x3/3 +
x5 /5 − ... + (−1)n−1x 2n−1/ 2n −
1 + Z x 0 (−1)n t2n /1 +
t2 dt.
(c) Show that tan−1 (x) − ( x...
I want to know when to use shell method and when to use washer method. and how to evaluate the improper integral. 1. Consider the region bounded by the graphs of f(x)-21 and g(x) 3-x2. 1.(a). (5 point...
I want to know when to use
shell method and when to use washer method. and how to evaluate the
improper integral.
1. Consider the region bounded by the graphs of f(x)-21 and g(x) 3-x2. 1.(a). (5 points) Write the integral for the volume of the solid of revolution obtained by rotating this region about the x-axis. Do not evaluate the integral. 24a). (I point) Is the integral dx an improper integral? 2.a). (1 point) Is the integral dx an...
1. Begin by making the substitution u=ex . The resulting integral should be ripe for a trig substitution. 2. Make a cho...
1. Begin by making the substitution u=ex . The resulting
integral should be ripe for a trig substitution.
2. Make a choice of trig substitution based on the ±a2±b2u2 term
you see after the substitution. With the right choice, after
substituting and rewriting using sin/cos, you should again have
something fairly nice to solve as a trig integral.
3. The substitution sin(2θ)=2sin(θ)cos(θ) is useful after you
integrate.
4. Don’t forget to back substitute (through several
substitutions!) until everything is in...
We have the following Limit Comparison Test for improper integrals: Theorem. Suppose f(x), g(x) are two...
We have the following Limit Comparison Test for improper integrals: Theorem. Suppose f(x), g(x) are two positive, decreasing functions on all x > 1, and that lim f(x) =c70 x+oo g(x) Then, roo 5° f(x) dx < oo if and only if ſº g(x) dx < 00 J1 (a) Using appropriate convergence tests for series, prove the Limit Comparison Test for improper integrals. (Hint: Define two sequences an = f(n), bn = g(n). What can you say about the limit...
Help on number 2 A-C Math 166 Spring 2020 Lab 12 - Integration Strategies and Improper...
Help on number 2 A-C
Math 166 Spring 2020 Lab 12 - Integration Strategies and Improper Integrals 1. Evaluate the following integrals. (a) | In(x2 + 2a) dx 100 dx (8) Jo Je to (1) ["* sin(a) Vsee(2) de 5 1 11 x² – 2x – 3 dx 87/2 13 x(lnx)2 de (c) / tarda (1) [4x*e*** de 2. For what values of p do the following improper integrals converge? (1/2 da (0) Le 2 In () Jo 3. Give...
Problem 3 Integrate: tan-12 du 1 + x2 Hint: This integral is improper! Begin by writing the improper integral as the appropriate limit. Then ask yourself: what is the derivative of tan-1x? (Show all details.) st
Question 2 please
1 and 2, determine whether or not the integral is In exercises improper. If it is improper, explain why 12. (a) 12 x-2/5 dx 「x-2/5 dx 「x2/5 dx (b) (c) I. (a) 0 13. (a 40 1 dx 2 x 14. (a In exercises 3-18, determine whether the integral converges or diverges. Find the value of the integral if it converges. 15. (a (b)人1x-4/3 dr 3, (a) l.lyMdx (b) x43 dx 16. (a 4. (a) 45 dx...
. (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...
tan-i (-1+-- 2. Express the limit lini Σ 2n 2 as a definite n 2n integral. Make sure to fully justify your work. Hint: What is equal to?
tan-i (-1+-- 2. Express the limit lini Σ 2n 2 as a definite n 2n integral. Make sure to fully justify your work. Hint: What is equal to?
Q9 (Approximation of π) (a)
Show that 1/1 + t2 = 1 − t2 + t4 −
... + (−1)n−1 t 2n−2 + (−1)n
t2n /1 + t2 for all t ∈ R and n ∈ N.
(b) Integrate both side in (a), show that tan−1 (x) =
x − x3/3 +
x5 /5 − ... + (−1)n−1x 2n−1/ 2n −
1 + Z x 0 (−1)n t2n /1 +
t2 dt.
(c) Show that tan−1 (x) − ( x...
I want to know when to use
shell method and when to use washer method. and how to evaluate the
improper integral.
1. Consider the region bounded by the graphs of f(x)-21 and g(x) 3-x2. 1.(a). (5 points) Write the integral for the volume of the solid of revolution obtained by rotating this region about the x-axis. Do not evaluate the integral. 24a). (I point) Is the integral dx an improper integral? 2.a). (1 point) Is the integral dx an...
1. Begin by making the substitution u=ex . The resulting
integral should be ripe for a trig substitution.
2. Make a choice of trig substitution based on the ±a2±b2u2 term
you see after the substitution. With the right choice, after
substituting and rewriting using sin/cos, you should again have
something fairly nice to solve as a trig integral.
3. The substitution sin(2θ)=2sin(θ)cos(θ) is useful after you
integrate.
4. Don’t forget to back substitute (through several
substitutions!) until everything is in...
We have the following Limit Comparison Test for improper integrals: Theorem. Suppose f(x), g(x) are two positive, decreasing functions on all x > 1, and that lim f(x) =c70 x+oo g(x) Then, roo 5° f(x) dx < oo if and only if ſº g(x) dx < 00 J1 (a) Using appropriate convergence tests for series, prove the Limit Comparison Test for improper integrals. (Hint: Define two sequences an = f(n), bn = g(n). What can you say about the limit...
Help on number 2 A-C
Math 166 Spring 2020 Lab 12 - Integration Strategies and Improper Integrals 1. Evaluate the following integrals. (a) | In(x2 + 2a) dx 100 dx (8) Jo Je to (1) ["* sin(a) Vsee(2) de 5 1 11 x² – 2x – 3 dx 87/2 13 x(lnx)2 de (c) / tarda (1) [4x*e*** de 2. For what values of p do the following improper integrals converge? (1/2 da (0) Le 2 In () Jo 3. Give...
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