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I lost in this I need help please thank you 12) [8] SET UP the surface...
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6) [8] с Use Green's Theorem to rewrite the integral [F.dr for the given vector field over the path C. F(x,y)=(x? In y, log; y+x’ tan-' x) and C is the boundary of the region D, bounded by the parabola x = y² and the line y=x-2. Assume positive orientation. SET UP the integral using Green's Theorem and include all bounds and variables of integration but DO NOT evaluate the...
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13) [6;10] Given F(x, y, z)=(-2yz, y, 3x), and C is the curve of intersection of z = 3x² +3y2 and z=3. Sketch a representative drawing. Assume C has counterclockwise orientation when viewed from above. (a) SET UP the line integral (F. dr as a line integral with a parameter t. Your final integral should be a с single integral in terms of t only, including the bounds of integration....
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8) [8] Given: E is the solid that lies below z = Vx² + y2 and inside x² + y2 + z2 = 5z. First describe what each surface represents, and sketch the solid. Then SET UP a triple integral using spherical coordinates to describe the volume of the solid. Explain clearly how you found the bounds for the spherical coordinates. DO NOT evaluate the integral.
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7) [10] Evaluate the integral using spherical coordinates. Sketch the solid of integration, and describe the solid in words. Evaluate the integral completely. SSL *Vx2 + y2 +2° dz dy de
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5) [8] Evaluate ds , where C is the curve y=-x4 1<x<2. 7 X
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+ 14) [12] Find the flux of the vector field F across the enclosed surface S. Sketch the surface. F = yi +3x j +4zk, and S is the boundary of the solid region enclosed by z=9-x² - y2 and the plane z=2. (note that this includes two surfaces). Assume outward orientation. Do not use the Divergence Theorem. Evaluate completely. Bonus 4 points Use the Divergence Theorem to solve the...
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aD 11) g Evaluate (y? +ex* ) dx + (3xy+cos y)dy where D is the closed semi-annular region above the x-axis between the circles of radius 2 and radius 5 centered at the origin (this is a “half-ring”). Assume positive orientation. Sketch the region and indicate the orientation along all pieces of the boundary.
3.0-14 points SCalcET8 82.005 Consider the following. (a) Set up an integral for the area of the surface obtained by rotating the curve about the raxis and the y-axis. (i) them is S= (i) the y-axits ) dy (b) Use the numerical integration capability of s calculator to evaluate the surface areas corract to four decimal places () the aeaxis () the y-axis Need Help? Tak to a Tuter
3.0-14 points SCalcET8 82.005 Consider the following. (a) Set up an...
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MTH705 Problems 4.... 4.3 Evaluate the line integral, ds where C is given by: x = t3, y = t4, 13ts 2 4.4 Evaluate the line integral, x?dx+y?dy where C is the line segment from (0,1) to (5,4) ype here to search O
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+ 9) [26] Given F(x, y)= (4x’e' + 3x?y?)i + (x*e” + 2x’y+y’e”); , (state any theorems you use!) [4;8;6;4;4] (a) show that F is a conservative vector field. (b) find a potential function f for F. (c) evaluate ( F.di where C is the line segment from (3,1) to (4,2). (d) if the curve...