Q3(a) Solve the integral below by using polar coor dinate and sketch the region 2-yt 2xy dxdy J-/2-y

Q: 6.4.12 Please help me solve these math practice questions.

A: Area of the curve y= cos(4x)  Where -π/8<x<π/8

Q: Evaluate the integral / (12x + 3y)dæ + (3x – y)dy along the parabolic arc y = x² from (0, 0) to (1,…

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Q: dy 1+ sin 4y

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Q: 8) By using the double integral in polar coordinate, find ,"[S" e-x²+y>dx]dy

A: The double integral in polar coordinates is given by the formula ∬Rf(x,y)dxdy= ∫ab∫g(θ)h(θ)f(rcosθ,…

Q: S tan-3 (x) sec² x dx

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Q: Evaluate the integral. 9. dx J2 (x² - 1 1)3/2 Additional Materials Type here to search

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Q: 8. By using the double integral in polar coordinate, find SS e-x*+y*)dx]dy

A: As we know that the polar coordinate: x=rcosθ,y=rsinθdxdy=rdrdθ Given: ∫0∞∫0∞e-x2+y2dxdy So, the…

Q: can you invent an exercise of double integrals with polar coordinates? to do it myself. (show the…

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Q: Calculate the integral (а) dx (*/3 Vtan 0 (b) п/4 -do sin 20

A: Given : (a)  ∫-∞∞x5e-x2 dx    (b) ∫π4π3tanθsin2θdθ

Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: Evaluate the integral. 1//3 3earctan(y) dy -V3 1 + y2

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Q: use a double integral to find the area of the shaded region.

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Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

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Q: Evaluate the integral / (10x + 15y)dx + (18x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Evaluate the integral (1+ etane) Sec?0 de

A: The given integral is, I=∫0π41+etanθsec2θdθ Let us solve the given definite integral using the…

Q: Evaluate the following line integrals in the complex plane by direct integration (not using…

A: Complex

Q: Calculate the double integral. 7x sin(x + y) da, R = [0, * [0, =]

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Q: T/2 10 r = 8 cos 20 5 - 10 -5 5 10 -5 - 10

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Q: Solve the equation by Cauchy's integral theorem. 1- dz 2- . 2z(4– z)dz

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Evaluate the integrals in Exercises using integration by parts

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

A: Solution is below

Q: Q₁) Find $dz 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using…

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Q: Evaluate the integral (12x + 6y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: п/2 (siny 1. dxdy 1-х2

A: We have to solve the integration

Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

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Q: Q21 Verify Green's theorem for $. (xy² + x²)dx + (4x – 1)dy where Cis shown in the figure by (a)…

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Q: Calculate the iterated integral.

A: To calculate the iterated integral ∫05∫142xy4+3dydx

Q: THE AREA BETWEEN THE CURVES 4 y = x²³² AND y ²³ = 4X IS REVOLED 2 ABOUT THE LINE X= -1. SOLVE FOR…

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Q: Evaluate the integral - T/2 (8 + 4cosx)dx 0. Using:

A: The given integral is ∫0π28+4cosxdx In part (a), we shall solve it analytically, and in part (b), we…

Q: Find the indefinite integral. Solution in handwritten. 1. secy (tany - sec y ) dy

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Q: Evaluate the integral (6x +12y)dx + (6æ — y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: Let us evaluate the given integral in the next steps.

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: Evaluate the integral (8x +9y)dx + (3x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: We can observe that x is ranging from 0 to 1. We have the following. So,…

Q: Q3: Evaluate the integral f xe dx by first finding the Maclaurin approximation to the integrand with…

A: The Maclaurin series: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Where centered at a=0 or x=0. Given:…

Q: Consider the following. dz 4z + 2 1 Find a substitution to rewrite the integrand as du. 4u du = dz

A: Given : ∫dz4z + 2

Q: Integrate f(z) = 1 counterclockwise around the unit circle, using 28 – 4.4 Cauchy's integral theorem…

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Q: Evaluate the integral. integral   sec 6  t  / tan 3t dt

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Q: 4 -dx is divergent. 1-2х (b) Show that the improper integral

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Q: aluate the iterated double integral. 1 cos(y) /5 + cos² (y) dydx Saresin (2)

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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: dy J y3-2y2 у3-2у?

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Q: -sin20 B)Evaluate the integrals: i) f/2 sinze rdrde, 0 ii) f/2/2 finx 2² siny dz dy dx. 0 0

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Q: Approximate the integral | dx using 4 trapezoids .2 1

A: Introduction: The formula for the trapezoidal rule is given by, ∫aby(x)dx=h2y0+yn+2(y1+y2+...+yn-1)

Q: 7. Find the indefinite integral. 1. dx V9-16x? 4x 1 tar arcsin 3 +C_b. arcsin(9x) +C a. 4 4x c.…

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Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

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Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

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Q: Use a double integral to find the area of the shaded region. -3 -1 π/2 -3 r = 2 cos 20 3

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