(a) 57/2² sin sin³ x cos³ x dx

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Q: √xdx 51. Evaluate Sv rationalizing substitution). x-1 . Hint: Use the substitution u = √√x…

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Q: Use Green's Theorem to evaluate the line integral of F = (x6, 4x)

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Q: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval…

A: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval [0,16)

Q: 3. f(x,y) = y²e²x – In(2x+5y) fx fxy fy fyx Show fxy = fyx

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A: By the answering guidelines of Bartleby, We can answer only first question from multiple questions,…

Q: Problem 3. Find the arc length of the semicircle y-√√9-x from (√5, 2) clockwise to (√5,2). (cf. page…

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Q: Consider the vector field F(x, y, z) = (6y, 6x, −z). Show that F is a gradient vector field F = VV…

A: The given vector field is:F(x, y, z)=6y, 6x, -z

Q: Write the equation in spherical coordinates:   x2 − y2 − z2 = 1

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Q: Find the area of the region that lies inside both curves r = 2 sin(20), r= 2 sin(0) 0 Area =

A: Area in the polar region is given by A = 12∫r2dθ Given function  r = 2sin( 2θ ) r = 2sinθ

Q: 1) Find the area of the triangle P(-2, -6, -1), Q (-2,-4, 1), R(3,6,6)

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Q: Select the correct choice below and fill in any answer boxes within your choice. OA. There are local…

A: Given function  f(x,y)= x2 + xy + y2 + 2x - 5y + 4

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Q: Use curl to determine whether the vector field (5xy, x² + 5y³z, y) is conservative. = (a) Find curl…

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Q: What is the 150th term of A 151 B с 152 309 9-1+29₁-11₂ "A-1

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Q: 4. (Section 17.6) Find inside x2 + y2 = 4. !!* d3 which gives the upward flux of F(x, y, z) =…

A: We have given that The given vector field is:F(x, y, z)=y, -z, 2xThe given surface is:z=4+y…

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Q: K The length of a stalactite (in mm) has been measured at the beginning of every fourth year since…

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