sin z dz, C (z+1)7 tan (z/2) ii) J. dz C Z-T/2

Q: Please evaluate the following line integral: Sc y? dx +2xy dy By parameterizing C as the line…

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Q: Evaluate the integral using integration by parts with the indicated choices of u and dv: -5t sec²(t)…

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Q: (1 dz z dx, 1 az z dxz 1 dz =x1 X2 X3. z dxz

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Q: Evaluate the line integral f y(tan x + x sec² x) dx + x tanæ dy + dz once around the circle x² + y²…

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Q: Let S be the shape obtained by rotating f(x) = 2 /x +1 on the interval [1, 3] around the x-axis.…

A: Given :fx = 2x+1

Q: The area of the finite region enclosed by the curves y = 3x and y 27 - a is given by the definite…

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Q: Set up an integral to find the area of the surface that is obtained by rotating the curve y = V4 –…

A: Here, y=4-x2, 0≤x≤1 is positive and has continuous derivative on 0≤x≤1. So, the surface area of…

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations.

A: First we need to find the x coordinates of the points at which the graphs of the functions…

Q: Let R be the shaded region bounded by the parabola y = 4 - x², and the lines y = 1- 2x and y= -1, as…

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Q: Without evaluating the integral, show that z dz <n where y is the semi unit circle in upper half…

A: To show that ∫γz dz ≤π we use the ML- inequality which is use ton estimate a complex integral. ML-…

Q: Evalunte the integral uSing the given change of voriabes. R Use X=4, y=2u +v

A: Firstly we can draw a region and find common region. Next we can find intersection lines and…

Q: Use symmetry to evaluate the double integral. Ja+ (1 + x8 sin(y) + y sin(x)) dA, R= [-π, π] x [-π,…

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Q: Assuming that the line integrals in the options are over the unit circle centered at the origin…

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Q: Sketch the region whose area is given by the definite integral. xp 3 2.5 yA.5 y 2 1 0.5 2 3

A: We can immediately discount the options on the right because the graphs are not of the function…

Q: Find an integral for the area of the surface obtained by rotating y = √25-x, 9 ≤x≤ 16, about the…

A: To find an integral for the area of the surface obtained by rotating the below equation about the…

Q: Set up the integral that calculates the area of the shaded region. r=3+2sinθ  r=2

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

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Q: Use an appropriate change of variable to evaluate the double integral: cos dA, R where Ris in the…

A: Given integral is  ∫∫Rcos(y-xy+x)dAR is the region bounded by x+y=1 ,x+y=2 in the first quadrant.

Q: Use Property 11 to estimate the integral xxD esin x cos y dA, where is thedisk with center the…

A: We know that –1 ≤ sin x ≤ 1 and –1 ≤ cos y ≤ 1, Hence, –1 ≤ sin x cos y ≤ 1

Q: line

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Q: 3) Show that the line integral is independent of path and then evaluate the inte S, sin y dx + (x…

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Q: Sketch the region enclosed by the curves x = sin 7y and x = 14 y, and compute its area as an…

A: Recall: Area between the curves :Given that x=f(y) and x=g(y) and f(y)≥g(y) on c,d, then the are…

Q: Find the inde finite integral using integration by parts with the given chaices of u and dv. X Cos…

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Q: Determine the integral of x y dx dy. Use inner limits=0 to (y + 1) and outer limits=0 to 1.

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Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: Evaluate the integral ∫sec z tan z/√sec z dz

A: Given: I=∫secztanzseczdz for evaluating given integral, in given integral we substitute secz=t…

Q: Is the integral A.dr path independant if A=(2x-y)i+(x+y)j? Evaluate closed line integral around a…

A: Given line integral is, ∮A.dr=∮[(2x-y)i+(x+y)j] dr  The condition for the path independence of a…

Q: 3) Show that the line integral is independent of path and then evaluate the integral: S. sin y dx +…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations y =…

A: Consider the following equation of curves: y=x32y=2x Intersection points of curves:…

Q: S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z?)dy + (3z² – 3xy + x² + 2yz)dz

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Q: Evaluate the line integral, where Cis the given curve. xyz? ds, C is the line segment from (-1, 4,…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the double integral where D is the triangle bounded by the x-axis, y-axis and the line y =…

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Q: Evaluate the integral starting from C of ydx + xdy+ zdz, where C is given by x=cost, y=sint, z=t^2 ,…

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Q: Evaluate the line integral. 17y dx + 16z dy +xdz, r(t) = (2+r',2,P) for 0 <t<1 (Give an exact…

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Q: the area of the region that is inside r=1 and outside r=1-cos(theta). set up the integral

A: Polar curve

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. y =…

A: Given data: The expression for the first equation is y=12x-x2. The expression for the second…

Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1. 3у?) dy

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Q: Let R be the disc of radius 1 centered at the origin, and let f(x, y) be a function. Express SSR…

A: Explanation of the answer is as follows

Q: Use an appropriate change of variable to evaluate the double integral: y- x cos y +x d A, R where R…

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

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Q: Compute the integral using contour integration: 27 cos no (cos 0+a)20 for a > 1.

A: Note:- ∫C fz dz =2πi ×sum of residues cosnθ= Re ei nθ  cosθ=ei θ+e-i θ2      Given that  ∫02π…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. X + dy

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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: Use an appropriate change of variable to evaluate the double integral: ソーx COS dA, y+ x R where R is…

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Q: dl /x² + y² + 4

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Q: Use the substitution formula to evaluate the integral. the integral from 0 to 1 (8y^2-y+1)^-1/3…

A: From the given integral, Let, 8y^2-y+1 = t ----(1)Now differentiating (1), 16y -1 dy = dt32y -2 dy =…

Q: Set up and evaluate the definite integral for the area of the surface generated by revolv y = 1x3 dx…

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Q: Use the calculus of residues to evaluate the improper integral COSX -dx. (x²+1)³

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Q: dydx tan x 1. 1+ y²

A: We need to calculate double integral in given order dydx   we use result of inverse Trigonometry…