1- Assume that x, y E R and z = x+ iy € C.Calculate the following integrals using the given contourand assuming that R - 00, 8 - 0 and Aø - 0.0o In(x)Jo Itx2a-CR0 Vxb- SoCE0 1+x2C2-R-E00 Vxc- So1+x20o In(x)d- So(4+x?)2co In² (x)е-2+x22ni E Residue = Sc +e,+og+G,(). Proveco. For S,(.) use z = egi® and evaluate the contribution from this term. For(Hint 1: Usethat Sa(..) = 0 as R →part e), first solve dx then expand log (2) function as (log|z| + iArg(=)*)In(x)2+x2(Hint 2: Here for log and sqrt functions the principal branch definitions can be employed.)

Answered: Image /qna-images/answer/2a362094-28e6-4e9d-b67c-32830cfd8e1e.jpg

1- Assume that x, y € R and z = x + iy € c.Calculate the following integrals using the given contour and assuming that R → 00, e → 0 and Ap → 0. 0o In(x) dx 1+x2 а- CR b- S. dx Jo 1+x2 -R 00 Vx

1- Assume that x, y € R and z = x + iy € c.Calculate the following integrals using the given contour and assuming that R → 00, e → 0 and Ap → 0. 0o In(x) dx 1+x2 а- CR b- S. dx Jo 1+x2 -R 00 Vx

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.2: Integration By Parts

Problem 3E

See similar textbooks

Related questions

Q: 4

Q: 1- Assume that x,y ER and z=x+ iy € C. Calculate the following integrals on C = {z:|z] = 1} contour.…

A: Residue theorem: If C is positively oriented simple closed curve and a1, a2,..., an are the point of…

Q: Evaluate the given line integral. | (y, -x) · dR, where C consists of the uppder part of x2 + y? = 1…

Q: 2- Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals…

Q: 1- Assume that x, y ER and z = x+ iy e C. Calculate the following integrals on C = {z: |z| = 1}…

A: Cauchy integral formula

Q: Set up an integral for the length of y = Vx + 2, 2<x<7 using ds : |1+ () dx. %3D A. ds = S, 1+ 1 dx…

A: Solution:Given y=x+2 2≤x≤7using ds=1+dydx2dxFormula:ddxxn=nxn-1

Q: 1- Assume that x, y E R and z = x + iy E C .Calculate the following integrals using the given…

A: Given :- Assume that x,y ∈ℝ and z = x+iy ∈ℂ. To determine :- The following contours :- (b)…

Q: Consider: dr, C: r(t) = (t, t²), te[0,1] Which one of the following "regular" integrals represents…

Q: Evaluate each of the following line integrals. Sc [(x² - y2)dx + (2xz)dy + (xy-yz)dz] where C: x =…

Q: 1- Assume that x, y ER and z = x + iy e C. Calculate the following integrals on C = {z:|z| = 1}…

A: Cauchy integral formula

Q: , (xy + 2)dV, 27. Calculate where B = {0 < x < 2, 0 <ys1, 1< z < 3} as an iterated integral in two…

A: Consider the following integral: ∫∫∫Bxy+zdVB=0≤x≤2, 0≤y≤1, 1≤z≤3 Consider the first way:…

Q: Determine the following integral dy y iny A y iny + C B. In (Iny) + C C. C In y+C D. D In'y+ C

A: Here, we have to evaluate the integral by "u-subtitution method"

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3…

Q: Suppose that f(r, y) = 2x + 4y at which {(x, y) |-1<a < 3, - 1<y< 3}. Then the double integral of…

A: ∫∫Df(x,y)dx dy=∫∫D2x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13x2+4xy3-1…

Q: Evaluate the iterated integral. TT V4 – z² z sin(x) dy dz dx

Q: Evaluate the line integral given in the figure below

A: Given question is belongs to the vector calculus and from the line integration we have to integrate…

Q: Compute the following integral: ez -dz z(z – 3) where y = {z : |z| = 2} positively oriented.

Q: 1- Assume that x, y E R and z = x + iy E C .Calculate the following integrals using the given…

A: Note: According to our guidelines We’ll answer the 3 subparts of the question since the exact one…

Q: Evaluate the following integrals. 1 (a) dz dy dx. e (b) TI Vx2 + y2 dV, where E is the solid in R3…

A: we have to find the integrals 1) ∫01∫01∫y1e-z2dzdydx 2) ∫∫∫Ex2+y2dV,where E is solid bounded…

Q: 1- Assume that x, y ER and z = x + iy E C. Calculate the following integrals on C = {z:|z| = 1}…

A: Use cauchy theorem for complex integral.

Q: 1-) Assume that x, y E R and z = x + iy e C and answer the followings. Calculate the reel integrals…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Suppose that f(x, y) at which {(x, y) |0 < x < 3, – x <ys vã}. 1+ x D Then the double integral of…

Q: 1-) Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals…

A: Given: (a) ∫-∞∞ x2x4+1 dx (b) ∫-∞∞ x2(x2+1)2 dx We have to calculate the (a) and (b)

Q: 1- Assume that x, y € R and z = x + iy € C .Calculate the following integrals using the given…

A: a) Given ∫0∞lnx1+x2dx ∫0∞lnx1+x2dx=12∫-∞∞lnx x-ix+idx=122πi Resi=πiln i2i=π2ln i=π2ln1+π2 i=π20+π2…

Q: Calculate the double integral of f(x,y) over the triangle indicated in the following figure: y 3…

Q: Set up a double integral to find the z = x? + y? %3! %3D z = 0

A: We are asked to set up double integral to find the volume.

Q: a) Evaluate the given integral In y In z dz dx dy 1

Q: (b) Let F(x,y) = (e2*y+cos(7x²), xºy^+e>Y³} Use Green's Theorem to set up the line integral F. dr as…

Q: Evaluate the given line integral. | (y, –x) · dR, where C consists of the uppder part of x² + y? = 1…

Q: Evaluate the Iline integral Jex*dx – xy dy +y² dz, where c(t) = (1, t, t² ), 0 < t s 1. Select one:…

A: The solution is given as

Q: Calculate the line integral of h (x, y) = (2xy) i + (x– 2ry) j; over r (u) = cos u i+ sin u j, u E…

A: Given function is hx,y=2xyi+x2−2xyj To compute the line integral over ru=cosui+sinuj from 0 to 2?.

Q: Suppose that f(x, y) D = {(x, y) | x² + y² < 9}. 6, and Then the double integral of f(x, y) over D…

Q: Compute the double integral of f(x, y) = 18xy over the given shaded domain in the following Figure :…

A: Given fx,y=18x5y

Q: Suppose that f(x, y) = e² / Y on the domain D = {(x, y) | 0 < y < 2,0 < x < y³}. D Then the double…

Q: 1- Assume that x, y ER and z = x + iy E C. Calculate the following integrals on C = {z: |z| = 1}…

A: By residue formula we can solve the problem

Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y? < 4}. Then the double integral of f(x, y) over D…

Q: Evaluate the following line integral I=[3x°dx + 2yzdy +y°dz from A: (0, 0, 0) to B: (2, 4, 8) a) By…

Q: Evaluate the following sum of iterated double integrals: 1 2y r2 r4-2y dz-a dx dy + Ax-a² dx dy e…

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: f(x,…

A: the double integral formula ∫x1x2∫y1y2f(x,y)dydx the value of y varies from 0 to 3 and the value of…

Q: Suppose that f (x, y) = 8x + 7y at which {(x, y) | – 2 < x < 3, – 2 < y < 3}. - D Then the double…

A: Use the integrating limit given on the set separately for x aand y

Q: 2- Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reel integrals…

A: a)The given integral is, ∫0∞1x2+1dx

Q: 1. Express the integral S S f(x,y, z) dzdxdy as an iterated integral in the other five different…

A: I1=∫02∫0y3∫0y2f(x,y,z) dz dx dy0≤y≤20≤x≤y30≤z≤y2I2=∫08∫0x3∫0y2f(x,y,z) dz dy dxx=y3,y=x30≤y≤x3y=0…

Q: Evaluate the iterated integral. In(x) xe Y dy dx dz 2z J3 Jo

Q: Evaluate each of the following line integrals. x dy – y dx, 2n <t< 4TT (a) c(t) = (2 cos(t), 3…

A: According to the given information it is required to calculate the line integral. For part (1)

Q: 1- Assume that x, y ER and z = x+ iy € C. Calculate the following integrals on C = {z:|z| = 1}…

A: We have to evaluate ∮C1z2−iz+34dz on C=z:z=1 Here, fz=1z2−iz+34…

Q: Match the correct representation of "u" to evaluate the given integrals by the method of…

Q: Evaluate the integral using any appropriate In2y dy y + 8y In y In ?y dy =] %3D y+8y In 3y (Турe…

A: Given : ∫ln2yy+8yln3ydy

Q: Let f(z)=4Re(z) and C be the line segment connecting 1+i to 0. Then the integral of f over C is…

A: Given function is fx=4Rez and C be the line segment connecting 1+i to 0 We have to find the integral…

Question

1- Assume that x, y E R and z = x+ iy € C.Calculate the following integrals using the given contour
and assuming that R - 00, 8 - 0 and Aø - 0.
0o In(x)
Jo Itx2
a-
CR
0 Vx
b- So
CE
0 1+x2
C2
-R
-E
00 Vx
c- So
1+x2
0o In(x)
d- So
(4+x?)2
co In² (x)
е-
2+x2
2ni E Residue = Sc +e,+og+G,(). Prove
co. For S,(.) use z = egi® and evaluate the contribution from this term. For
(Hint 1: Use
that Sa(..) = 0 as R →
part e), first solve dx then expand log (2) function as (log|z| + iArg(=)*)
In(x)
2+x2
(Hint 2: Here for log and sqrt functions the principal branch definitions can be employed.)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Triple Integral$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.