Let I = [[e2 dy dx. -2y 0 x Evaluate the integral (in the given order of integration). Use the sketch from the chalkboard to set up I in the other order dx dy. Use the sketch from the chalkboard to set up I in polar coordinates. А. В. С.

Q: Evaluate the following integral in cylindrical coordinates. 2 14-x2 1 dz dy dx -2 0

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Q: Q4: Convert the following polar integral to Cartesian Integral in order (1) dx dy (2) dy dx T 6 csc0…

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A: Integrate as general

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A: Convert the given integral.

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A: Solve

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Q: Change the Cartesian integral to an equivalent polar integral and then evaluate: 225-y² (x² + y²) dx…

A: ∫015∫0225-y2x2+y2dxdy=50625π8

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A: The given integral is

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Q: evaluate the iterated integral.

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Q: Evaluate the following integral in cylindrical coordinates. 1 1-x2 2 1 dz dy dx 1 + x2 + y? -1 0

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Q: Evalute the following integrals using Polar method: a √a²x² $5 Jy dx √a²-x²

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A: We will find out the required value.

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A: Let,      I=∫0π2∫0π2sin(x+y)dydx

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 1 dy dx - 5 25-x2…

A: Convert given Cartesian integral to polar integral using substitution and evaluate this integral

Q: Evaluate the line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0,…

A: Given: ω=xydx+12ydy To find: I=∫αω  where α:[0,ln2]→ℝ2 with α(t)=(e2t,e-2t) ∴x=e2t,y=e-2t Now,…

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. dy dx -5 V25- x-…

A: The given x and y limits i.e. x=-5  to  x=0      and      y=-25-x2   to    y=0 define the domain of…

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Q: Evaluate the iterated integral given below

A: The given question is from the calculus and subcategory of the double integration we can solve this…

Q: (a) (x2 + y?) dx dy J2

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Q: 36 ll a O HD 57% D 8:42 2_52782976274... Evaluate:- siny dx dy SS (3-6x)dA, here Dis the region…

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Q: -In 3 c(In 3)2 - y2 Z +y? dx dy a) Sketch the region of integration b) Express the region in polar…

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Q: Evaluate the following integral in cylindrical coordinates. 2 14-x x2 + y2 - 1/2 dz dy dx 0 0

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Q: Evaluate the iterated integral. (x + y) dy dx

A: We have to solve given double integral

Q: Let p (x +e*siny) dx + (x +e* cos y)dy be the line integral on the boundary of the triangle enclosed…

A: To find the equivalent double integral we will use the Green's Theorem also we will draw the…

Q: Use polar coordinates to combine the sum 1 2 4-a2 xy dy dx + /1-x² xy dy dx + Xy dy dx into one…

A: Given,   ∫121∫1-x2xxydydx + ∫12⏟ ∫0xxydydx + ∫22⏟ ∫04-x2 xydydx⏟                          I1…

Q: - Evaluate the integral 4-z²-y² 1 dz dy dx Jo 4-z²-y² x² + y² + 2² using spherical coordinates.

A: To evaluate ∫-22∫04-x2∫-4-x2-y24-x2-y2 1x2+y2+z2 dzdydx

Q: Calculate the iterated integral. '1 I l'x+e-Y) dx dy Need Help? Read It

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Q: Find the value of 1-1/16 (x² + y²) dy dx + ſ', [~ ² * (x² + y²) dy de by expressing it as one…

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Q: Evaluate the iterated integral. V81-y y dx dy = i %3D

A: Solution is given as below:

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A: I have done solution in detail...go through the solution

Q: Calculate the iterated integral. 5xyV x? + y? dy dx

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Q: 2. Convert the following double integral to polar coordinates and evaluate. S so dx dy 4y-y² Jx²+y²…

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Q: Calculate the iterated integral. '64 Y)dy dx

A: Given that a double integration and we solve this using general rule of integration. Here i attached…

Q: /2 TT Sin (x ty) dy dx 0

A: Consider ∫0π2∫0π2sin(x+y)dydx = ∫0π2∫0π2sin(x)cos(y)+cos(x)sin(y)dy dx =…

Q: to polar coordinates turns into an integral S S" x² + y² dxdy When converting the integral

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Q: Evaluate the double integral: cos(y') Vy3 dy dx.

A: The solution is given as

Q: Change to polar integral S e (z²+y?) -1 -V1-r? V1-x² o ° re-rdrde So' So re- drde O S: So re drde S:…

A: The solution is given below in the next step:

Q: Consider the following line integral. xy dx + x?y dy, Cis counterclockwise around the triangle with…

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Q: Calculate the iterated integral. (x + y)² dx dy

A: In the question we have to find integral of the given function.

Q: T/2 T/2 (b) sin(x + y) dy dx

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Q: Evaluate the integral S 4-y2 dx dy using polar coordinate

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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 10 V100-y2 (x2.…

A: ∫-1010∫-100-y2100-y2 x2+y252dxdy Sketch the region -100-y2≤x≤100-y2

Q: Calculate the iterated integral

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

Q: Use Green's Theorem to evaluate the line integral. e cos(2y) dx - 2e* sin(2y) dy C: x2 + y? = a?

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Q: Evaluate the integral: L x2 + y² dy dx by using polar coordinates.

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