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

Q: first octant 2 4- x+y dy dx -

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Q: Evaluate the double integral over the rectangular region R. / 8xy°dA; R = {(x, y): – 1 < x < 1, – 7…

A: Given:       ∬R8xy6dA   R=x,y: -1≤x≤1 , -7≤y≤7        ∬Rfx,ydA=∫ab∫cdfx,ydydx…

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: Show

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A: We have to find it from Trapezoidal rule.

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A: A detailed solution is given below

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

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Q: Question 6 Evaluate JJ xy dA, where R is the region in y = x2 R A) 13/7 B) 16/3 18 20 2.

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Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = TT, using 4…

A: Here, the interval [0,π] is divided into 4 intervals of the length of each interval is ∆x=π-04=π4.…

Q: Current Attempt in Progress Sketch the curve by eliminating the parameter, and indicate the…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 51…

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Q: Sketch the region enclosed by the curves and find its area. у %3 сos 9x, y —D 0, х - x = 18' 9 NOTE:…

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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: The point (– 1, 3) is on the terminal side of 0 in standard position. The exact value of cos(0)is…

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Q: Find the equation of the line perpendicular to through (7, 2) through (-1,7/2) through (1/3, 13)…

A: The line perpendicular toa) 2y-3x=1 through 7,2b) 9x+15y+6=0 through -1,72c) x+y=1 through 13,13…

Q: Find the area of the region bounded by the graphs of f (x) = x³ and g (x) = x. (A) 1 c) 0.5 3.

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Q: Question 20 Evaluate JJ xy dA , where R is the region in y = x? R (A) 13/7 (в) 16/3 18 D) 20 2.

A: We have to find the area.

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Q: bounded by the graphs of the equat y

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

A: Here, to find the volume if the solid enclosed by: x2+y2+z2=4a2 The cartesian to spherical…

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A: We have to find the volume by shell method.

Q: e

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Q: Find the area of the region(s) enclosed by the curve f(x) = x°, the x-axis, and the lines x =-1 and…

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Q: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

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Q: 2а-2х V4a-V4x

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

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Q: Find the exact arc length of the curve over the stated interval. 1 1 Gy, from y =1 to y = 3 12 NOTE:…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 6…

A: A detailed solution is given below.

Q: Use double integration to find the volume of the solid bounded by the paraboloid 2 = 9X- + y, below…

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Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

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Q: dx dy =

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: Evaluate the triple integral. /I| ry sin(yz) dV, G where G is the rectangular box defined by the…

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Q: In sketching the graph of y=f(x) = 2sin -5, we translate the graph of y=2sin by 5 units downward and…

A: To translate the given function.

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: 4 y=V4x- 2/2x

A: Topic = Derivative

Q: Find V · (V × F) if F(x, y, z) = 4 sin xi + 8 cos(7x – 8y)j + zk. V: (V × F)

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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: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 B) 9 12 15

A: Let's find.

Q: Use the arc length formula to find the length of the curve y = 3x - 5, -2 SxS 3. Check your answer…

A: This question is related to Functions and curves, we will solve it using given information.