Carry out the transformation x = sin 0/cos Y y = sin o/cos 0 on the triangular region {(0, 4); 0, y > 0, 0+ y < n/2} in the improper double integral dxdy 3 3(2) = 1– x²y² ' where S is the unit square [0, 1) × [0, 1).

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Q: ntegral Sa F . 0) & (1, 1)

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Q: C Jxe-2* 9. Evaluate the integral using property of the PDF: So Vxe²*dx 10. Suppose x = Exp(^), Show…

A: Since you have posted two questions, we will do only first question as per our guidelines. Thus,…

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Q: 8.(6 pts) Use Fundamental Theorem of Line Integrals to compute / Vf - dr where f(z, y, z) = ry? +…

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Q: Show that (2x In yz-5ye") dx-(5e* -x²y)dy +(x²z- +2=) dz, where C runs from (2,1,1) to (3,1,e), is…

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Q: A new flag pole for a school campus measured 25 2/3 feet. It was put 4 1/2 feet into the ground and…

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Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

Q: a) Evaluate the line integralZ F dr C in terms of t where F = cosyi+xj+ye²>k and C is the line…

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Q: 7) Evaluate the integrals a) 3(x + 1)²dx b) secx (tanx +cosx )dx

A: An indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that…

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A: The given vector is F=3x2yi+x3j Here we use Green's theorem. So the Green's theorem is…

Q: By converting to polar form, integrate the In(x? + y?) x2 + y? function f(x, y) over the region 1…

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Q: { e, a| 1, The Fourier integral of f (x) = %3D A) roo w sin w-cOS w sin zwdw w2 roo sin w-CoS W sin…

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

A: Line integral will be path independent if vector field whose integral we need  is conservative…

Q: a) Plot a direction field and some integral curves  for xy'-2y=-1 on the rectangular region {-1<or…

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Q: Evaluate the line integral ∫(AB) xdx+ydy+zdz using the fact that the integrand is a perfect…

A: Here we find ∫(AB) xdx+ydy+zdz,   by using the fact that the integrand is a perfect differential. A…

Q: evaluate the contour integral z^2 -z^4/z-1)cos(z)where c:|z|=4

A: Introduction: Cauchy's integral formula is very significant in complex analysis. It helps to…

Q: Use Green's theorem to evaluate the line integral I of the one-form W = + æ sin? (y)) dæ + (x²…

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Q: Verify Green's Theorem for Jo where C' is a triangle with vertices (0,0), (1, 3), and (1,5) traced…

A: Let  be the vector field and C be the boundary of the region D.The Green's theorem states that…

Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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