Find the exact arc length of the curve over the stated interval. 1 -2, from y = 1 to y = 2 1 49 NOTE: Enter the exact answer. L =

Q: Evaluate the double integral over the rectangular region R. || xV16 – x*dA; R = {(x. y): 0 < x < 4,…

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Q: Find the point of intersection (xo, Yo, zo) of the lines given as: y = 4 + 5t, z = 2 + t z = 3 + 21…

A: To find the point of intersection x0, y0, z0 of the lines given as: L1: x=7+t, y=4+5t, z=2+tL2:…

Q: d Calculate ri(t) · r2(t)] and d dt [r1(t) x r2(t)] first by differentiating dt the product directly…

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Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X y² +…

A: We have to find the volume of the solid.

Q: Find the volume of the solid that results when the shaded region is 7 revolved about the indicated…

A: Use the washer method to find the volume of rotation of the solid.

Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

Q: Use a double integral to find the volume under the plane z = 22x + yand over the rectangle R = {(x,…

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Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

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Q: Evaluate the iterated integral. x dz dy dx 128/15 16/89 23/6 6.

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Q: f(x)= 2cos (x) − 6sec (x)+3 =

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Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

A: Given:          Curve y=2x2+10                     y=4x+16

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Question 6 Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 A) 6 B) 9…

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed.…

A: Express the iterated integral as an equivalent integral with the order of integration reversed.

Q: Find the approximate area under the curve of f (x) =x+1 from x = 0 to x = 2, using 4 left-endpoint…

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Q: r2 cose dr de valuate the iterated integrals A) 1

A: ∫0π∫01-sinθr2cosθdrdθ

Q: Find the center of mass of the given system of point masses lying on the x-axis. - 6, - 3, m,- 6 X1…

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Q: n/2 sine Evaluate the iterated integrals r cos e dr de 0.

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Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-2 and y=x about…

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Q: Evaluate the double integral over the rectangular region R. y'dA; R = {(x, y): -1sxs1, - 8 <ys 8} |…

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Q: Question 2 Use spherical coordinates to find the volume of the solid. The solid enclosed by the…

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Q: for the given path. C: x = 2 cos(8), y = sin(@), o se s 27

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: (b) Evaluate the velocity vector and acceleration vector of the object at the given point. %3D %3D…

A: As you mentioned part b is solved

Q: Determine the work done by the constant force. The locomotive of a freight train pulls its cars with…

A: Given data÷

Q: Evaluate the line integral / (2x + 7y)dx + (4x – 6y)dy along the curve C: = 6 cos t, y = 12 sin t…

A: Let's find.

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -162 -108

A: ∫02∫-162y2∫-108zyz dx dz dy∫-108zyz dx=(xyz)-108z…

Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) R (2, 1) (4, 1) A) 56 В) 67 с) 38 90

A: Explanation of the answer is as follows

Q: Evaluate the double integral. 7x*sin y²dA; Ris the region that is bounded by y = x³, y = -x³, and y…

A: double integral

Q: Find the area of the region inside the circle r = 18sinθ and outside the cardioid r = 6 + 6 sinθ.

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Q: <press the area of the given surface as an iterated double integral, and then find the surface area.…

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Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

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Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt dt the product directly…

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Q: Evaluate the iterated integral. 6 7 8 /// (x² + y² + z²) dxdydz -6 0 0 6 7 8 (x² + y² + z?)dxdydz i…

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Q: FOTE: Enter the exact answer. dx dy = VT

A: A detailed solution is given below.

Q: Describe the graph of the equation: r = 5ti – 8j + (1 + 5t)k. [Choose the correct answer.] O The…

A: Given, r= 5ti -8j +(1+5t)k Therefore, The equation is given by, r= &lt;0,-8,1&gt;+t&lt;5,0,5&gt;

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

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Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2

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Q: Determine the volume of the solid obtained by roteting the region bounded by y=x^2-2 and y=x about…

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Q: Evaluate (2x – y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (8, -5) Need…

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Q: Using appropriate substitution xp: V9x2-36x + 37 Is equal to

A: We have to integrate given function

Q: sine "/2 Evaluate the iterated integrals r cos e dr de A 1/6 1/2 11/9

A: Explanation of the answer is as follows

Q: Find the length of the curve, L. y? = 64 (r+ 5)* , 0 0

A: To evaluate the length of the given curve.

Q: V4-x? 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x2+y? A 128/15 16/89 23/6

A:

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy = -72

A: To evaluate: ∫02∫-72y2∫-48zyz dx dz dy

Q: В. 5. We let y(t) be the position function. What is the position function? A. p(t) = - 16t2 - 100 t…

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Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Evaluate the definite integral. 14t i + e*j+t k)dt (el4 – 1) i – (e-1 – 1) j + k 1-(6" -1) + i- (e~-…

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Q: ||r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 3 r(t) = t'i + tºj %3| K(t) =

A: Use the given formula and find the required expression.

Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.