dz ; C is a circle Iz-1| = 1/2 z4-1 z2

Q: а. Find the integral of e42 dz, where C is a circle z-2= 8 and x 1+ last digit of your ID.

A: In the given question we have to calculate the integral I=∮Ce4z(z-x)6dz where C is circle z-2=8 and…

Q: 0. Everlueik he integral (ez)Esmz dz, where Ci12|=1, by any and two methods Compare the geselts.

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Q: Sketch the curve y cu. = x sq.   Use Formulas 3 and 4 to set up two integrals for thearc length from…

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Q: For the integral xe2x) dx what is u? Note: no space between symbols in your answer

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Q: Find a formula for the integral. dy = y 3(1– 6y) Incorrect

A: We have ∫e6xe3ydy

Q: Evaluate the line integral -ydx + xdy along the curve C: = = 21x from (21, 21) to (0,0). %3D NOTE:…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. (y – x) dx +…

A: Explanation of the answer is as follows

Q: Evaluate the integral. Scos* (40)de

A: Given integral is ∫cos44θdθ Substitute  4θ=u ⇒dθ=du4 Hence,…

Q: Set up, but do not evaluate, an integral for the length of the curve. y = x - 4 In(x), 1sx s 4 dx

A: Topic - length of curve using integrals

Q: Area = 2c 27 dx

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. (y - x) dx +…

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Q: Q3 Evaluate the integral fei sin e dz, where Cis a circle |z| = 1.

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Q: Next, use the substitution w = x² – 9 to find the integral: SZ, da = S 1/w dw = In(w) +C =…

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Q: Sketch the region whose area is represented by the definite integral. dx y 12 12 10- 10 8. 6 6 10 2…

A: The definite integral can be used to evaluate area of region bounded by curves. If over an interval…

Q: ): The integral that represents the length of the curve y = e, where 2 <<4, %3D is the following:…

A: Let given integral be I , then we get  I = π∫24e10xdx Now calculating the value of intergral  ⇒I =…

Q: Is the integral / A · dr path independent if A = (2x - у)i + (x + у)j? Evaluate A · dr around a unit…

A: The question has 3 subparts. 1st part requires the verification for path independence of a line…

Q: What is the integral that represents the length of the curve from x = 2 to x = 4. Select one: 0 ₂²…

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Q: Evaluate the line integral along the path C given by x = 6t, y = 24t, where 0 tS 1. (x+3y²) dy Need…

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Q: Using a Table of Integrals with the appropriate substitution, find ſešz + 2e2z + 8e de Ve2x – 36

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Q: 3) Write the integral that equals the area of the surface formed by rotating the curve x = 1 + 1s y…

A: Write the integral that equals the surface area of the given curve rotating about x-axis

Q: Evaluate the integral 4 (y 2)(2y1) dy Jo

A: To evaluate,

Q: 2. Evaluate the following integrals. (b) L, sin y² dy dx

A: Let us consider the double integral I=∫D∫f(x,y)dA, where D is the region of the integral.   The…

Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Use a double integral to find the area of the region outside the circle r = 5 but inside the circle…

A: Given information is: Outside the circle r=5 and inside the circle r=10sinθ. Calculate the area of…

Q: Consider the following. x = ? - 2t, y - t*, 1sts4 Set up an integral that represents the length of…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. + 3у?) dy

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Q: Please solve the given line integral which is the following: Se(x² + y²) dx – x dy In where C is the…

A: The given line integral is: L=∫Cx2+y2 dx -xdy where C is the arc of quarter circle that is going…

Q: (241) dz (24)(러3)(2)

A: Solution:

Q: Evaluate the line integral - y² dx, where C is the square cut from the first quadrant by the lines x…

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Q: Evaluate V16-x² dx dx be? Explain Then, what would the value of the integral 1+V16-x 0.

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Q: 2 sin 0 r dr d0 T/2 Jo

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Q: Evaluate the double integral /| sin(z² + y*)dA where D is the bottom half of the circle x2 + y² = T.…

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Q: The integral (*, y) dy da is to be evaluated with respect to Ox first, the y. O None of these Oy…

A: First Y then X  Option c.

Q: The length L of the curve 4y? = (4x – 3)3, 2 0, is given by the integral, .3 Ax² + Bx + C dx 2 and…

A: It is given that - The length L of the curve - 4y2=(4x-3)3  , 2≤x≤3where y≥0 is given by the…

Q: 2y-ya Evaluate the integral 12 + y?dzdydr by using cylindirical coordinates.

A: Let z = z , x = r cos(theta) , y = r sin(theta).

Q: 3) Write the integral that equals the area of the surface formed by rotating the curve x = 1+ 2y2, 1…

A: Recall: If the curve is given by x= g(y) ,c≤y≤d and rotated about the x-axis , then the area of the…

Q: Sketch the region whose area is represented by the definite integral. ▪4 5 dx y y 6F

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Q: Evaluate the integral. V3 9earctan(y) dy 1 + y2

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Q: 1-2 a + y+z dzdxdy 0.

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Q: 1. What should be A for the path independent of (2,4) ry + ) 2Ay – x dy y? dx+ (1,2) Moreover…

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Q: The improper integral J 1 r2-4x-5 dx is given by:

A: In this question, we reduced the integral into trigonometric form by using suitable transformation.

Q: Which ONE of the following integrals correctly represents the area of the surface of revolution…

A: giveny=ln(x5)rotation about x-axisA=∫152πyds

Q: Set up, but do not evaluate, an integral for the length of the curve. xex⁹ Jo y = 0≤x≤5 dx

A: Given,  y=xex9, 0≤x≤5

Q: Find the value of the integral of g(z) around the circle |z – i| =2 in the positive sense when g(2)…

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Q: çin fxa-lex®dx dx 3?

A:

Q: Set up, but do not evaluate, an integral for the length of the curve. y = x – 9 In(x), 1sxs 4 dx

A: The integral for the length of the curve is  L=∫ab1+dydx2dx

Q: Is the integral / A · dr path independent if A = (2x - y)i+ (x + y)j? of Evaluate A · dr around a…

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Q: The value of the integral dz, over the Contour C |2- 2| = 2 is equal :- 2

A: Cauchy's integral function: Suppose C is a simple closed curve and the function f(z) is analytic on…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. (y – x) dx +…

A: We need to find integral value.

Q: The improper integral A) e (В (C) O (D) 1 8 Stoe ex dx is

A: We have to find the value of the integral