Calculate the integral of f(x, y) = 10x over the region D bounded above by y = x(2 – x) and below by z = y(2 – y). Hint: Apply the quadratic formula to the lower boundary curve to solve for y as a function of r. Answer :

Q: Evaluate the integral| c. ff sin x dA; R is the region bounded by the lines y = 2x, y = x and x = .

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Q: Verify Green's Theorem by evaluating both integrals dk + x° dy = /. / dA ду for the given path. C:…

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Q: The value of the triple integral 2x² dV E where E is the region inside both x² + y? + z2 : z = -V3x2…

A: Here we will use cylindrical co ordinate to find triple integral  in cylindrical co ordinate  x = r…

Q: Use the substititutions и — у — х, and v 3 y + 2x to evaluate the integral - (2х + у) (х — у) dx dy…

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Q: Verify Green's Theorem by evaluating both integrals |y? dx + x² dy = ƏN aM dA əx for the given path.…

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Q: Verify Green's Theorem by evaluating both integrals y² dx + x² dy = / dA дх ду for the given path.…

A: Here we have to verify the Green's theorem.

Q: Evaluate the following integral: b.) !!!! xyz dv if S is the region bounded by the cylinders ² + y²…

A: According tot the given conditions the limi values of x,y and z are0≤x≤50≤y≤25-x20≤z≤25-x2Hence…

Q: Evaluate the triple integral. SSSE2.xy dV , where E lies under the plane : = 1+x + y and above the…

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Q: Evaluate the double integral / (3x + 2) dA I D when D is the bounded region enclosed by y = x and y…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Verify Green's Theorem by evaluating both integrals ƏM ? dx + x² dy dA ax ду for the given path. C:…

A: Given : ∫c y2 dx + x2 dy , Where, c : boundary of the region lying between the graphs of y =x &…

Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: Use Green's Theorem to evaluate the line integral. dx + xy dy C: boundary of the region lying…

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Q: Evaluate the double integral + y? )dædy, where N is a bounded region between y = x² and y = x³.

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Q: Evaluate the integral of the two-form w = (a* + 4y) dx A dy over the region D bounded by the curves…

A: Solution:-

Q: Find the area enclosed by the loop in the graph of the curve E: x(t) = t?, y(t) = t³ – 3t by…

A: To find - Find the area enclosed by the loop in the graph of the curve C : xt = t2, yt = t3 - 3t by…

Q: Use Green's Theorem to evaluate the integral In(x2 + 1)dx – xdy, C is the boundary of the region…

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Q: Verify Green's Theorem by evaluating both integrals ƏN ƏM v? dx + dA ду dy %3D Əx for the given…

A: We have to verify the green's theorem by evaluating both integral ∫Cy2dx+x2dy=∬R∂N∂x−∂M∂ydA, where…

Q: Evaluate the integral of the two-form w = (x8 + 2y) dx A dy over the region D bounded by the curves…

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Q: Verify Green's Theorem by evaluating both integrals ƏN y2 dx + x² dy dA ay for the given path. C:…

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Q: 3. Use Green's Theorem to evaluate (e3x +y²)dx + (sin y – x²)dy where C is the boundary of the…

A: Green's theorem

Q: Evaluate the triple integral. 3xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: evaluate the triple integral given by fff (x + 2y)dV, where E is bounded by the cylinder y = x² and…

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Q: Evaluate the integral [[[var !!! y² dv where G is the solid in the first octant that lies below the…

A:

Q: Evaluate the double integral I = | | (2 – cos(x + y)) dA D when D is the bounded region enclosed by…

A: Given- I=∬D2-cosx+ydA, where D is the region bounded by the lines x+y=π,x=0 and y=0 To find- The…

Q: Use Green's Theorem to evaluate the line integral. y2 dx + ху dy C: boundary of the region lying…

A: Use green s theorem

Q: Evaluate the triple integral. 2xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Final answer is 65/84.

Q: 1. Let A be the region enclosed by the curves y = r² + 1, y = (2x – 1)² and r = 1. 2 ty y = x² +1…

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Q: Evaluate the double integral 4.x dydr 9 + y2 I when A is the shaded region in enclosed by the graphs…

A: Evaluate the double integral.

Q: Verify Green's Theorem by evaluating both integrals aN y2 dx + x2 dy dA ду - əx for the given path.…

A: For c-1 sign is negative because of opposite direction

Q: Use Green's Theorem to evaluate the line integral. for y2 dx + xy dy C: boundary of the region lying…

A:

Q: Evaluate the triple integral. SSSE 7xy dV¸ where E lies under the plane = 1+x+ y and above the…

A: We have to Evaluate the triple integral.

Q: Verify Green's Theorem by evaluating both integrals (ON-OM) d [[ y² dx + x² dy = √ √ ( ³x for the…

A: In this question, we want to verify the green's Theorem for the given integral.

Q: Evaluate the triple integral. 7xy dV, where E lies under the plane z = 1 + x + y and above the…

A:

Q: Use Green's Theorem to evaluate the line integral. J. 2xy dx + (x + y) dy C: boundary of the region…

A:

Q: (a). Evaluate the following integral by using the Green's Theorem {(e* +x°)dx+ (e* +x²)dy where C is…

A: Green's theorem

Q: Verify Green's Theorem by evaluating both integrals |y? dx + x2 dy dA ax ду for the given path. C:…

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Q: Verify Green's Theorem by evaluating both integrals | y² dx + x2 dy dA ax for the given path. C:…

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Q: ; Evaluate the triple integral Answer: II z dV, where E is bounded by the cylinder y² + z² = 9 and…

A: evaluate the triple integral ∫∫∫Ez dV where E is bounded by the cylinder y2+z2=9 and the planes x=0…

Q: Use Green's Theorem to evaluate the line integral $. (x2-y2)dx + (2y -x)dy where C consists of the…

A: We will plot the region bounded by two given curves and find the integral using Greens theorem

Q: Use Green's theorem to evaluate the integral: 6(-x²y)dx + xy°dy where C is the boundary of the…

A: Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region…

Q: Use Green's theorem to evaluate the integral for S[(6y-e*) dx +(8x+ lIn(4y)) dy]. where C is the…

A: Evaluate the integral              ∫C6y-e3xdx+8x+ln(4y)dy using Green's theorem, where C is the…

Q: Verify Green's Theorem by evaluating both integrals dA ? dx + x c dy Əx ay, for the given path. 2 C:…

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Q: Define R as the region bounded by the graphs of f(x) = 2√x and g(x) = over the interval [0, 1].…

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Q: Evaluate the triple integral. 4xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: Use Green's Theorem to evaluate the line integral. S y² dx + xy dy C: boundary of the region lying…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: Evaluate the triple integral. SITE3*y dV, where E lies under the plane = 1+x + y and above the…

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Q: Evaluate the line integral [2y'dx+(x* +6y°x)dy where C is the boundary of the R region shown below…

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Q: Verify Green's Theorem by evaluating both integrals an_ am | v² dx + x² dy = dA ây for the given…

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