Sketch the region of integration and change the order of integration. 3 19-y² f(x, y) dx dy f(x, y) dy dx

Q: y = 4 − x2,    y = 0 Calculate its area

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Q: 3. f(x, y) dx dy f(x, y) dy dx

A: ∫03∫0yf(x,y) dx dy=∫03∫x3f(x,y) dy dx

Q: 65. y = 3x - x3, x = 0, y = 2 are bounded in the first quadrant. Determine its area. % sq. units %3!

A: Given: when y=2, we have 2=3x-x3⇒x=1. Now, dydx=3-3x2. So,            S=2π∫01 1+3-3x22dx  =2π∫01…

Q: y y = x' - 2 x 4 2 -4 -2 2 -2 y = 2 x -6F (a) Find the points of intersection of the curves. (х, у)…

A: We have to solve given problem:

Q: Evaluate cex-y) dx + C (x+3Y) dy C:xaxis from (0,0) to (0,-3) and 0-3) to (5,-3).

A: To Evaluate: ∫C2x-ydx+x+3ydyC: x-axis from 0,0 to 0,-3 and 0,-3 to 5,-3.

Q: dy / dx i

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Q: 4. Integration by Inspection y (2xy+ y²) dæ + x (y² – x) dy = 0

A: Differential equations

Q: 1 64 cos(64tx7) dxdy 1 'y6

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Q: f(x, y, z) = tanxy xy;f,(1, 2, -2) %3D

A: Dear student, since you have posted multiple questions, as per our policy we will answer first…

Q: Find f(x, y) dx and f(x, y) dy. f(x, y) = 5x + 3x?y² f(x, y) dx = %3D 3 f(x, y) dy %D

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Q: dw 3. If w = f(x, y, z), g(x, y) = C₁, h(x, z) = C₂ find: dx constants. c1& c2 are

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Q: v(v² –1)dv v2 +1 3.

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Q: dy Using variable separable method find y from dx = 3y 2x+1

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Q: c) Integrate the function f(x, y) bounded by the lines y = x, y = 2x. x = 1. r = 2. over the region…

A: Integration over the said region

Q: substitution. Why is the answer Y - 2 In l Y + 1 l + C

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Q: Coute : 2y da + 3x dy, where D is described by 0 < a < 1, 0 < y < 1.

A: We have to find the given integral. For this we can use Green's theorem

Q: Evaluate the integral dx (2x + 6) by making the appropriate substitution: u = dx (2a + 6)°

A: To evaluate the given integral.

Q: dy y X, dx

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Q: JS xy dA R: rectangle with vertices (0, 0), (0, 3), (5, 3), (5,0) 166xx 16 xy dx dy = xy dy dx =

A: The solution is given as

Q: If a field K is algebraically closed, then every polynomiel with co efficients in k has a root in K.…

A: A field K is said to be algebraically closed if every polynomial with coefficients in K has a root…

Q: he The product of linear integration is where c t $ (2xy – x²) dx + (x + y²)dy, x = y? 30 y = x? ,…

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