Calculate the volume of solid of revolution when the region bounded by y = sin 2x and x² - y2 = 0 is revolved about the line y + 4 = 0

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A: Explanation of the answer is as follows

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A: a) y=cos x, 0, 3π2b) y=x2+x+1, 0,1

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A: As per bartleby guidelines we only give first question answers.

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A: Solve by matrix

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A: Given that∫25fxdx=12 and ∫58fxdx=4Solution :a.∫28fxdx=∫25fxdx+∫58fxdx                 =12+4…

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A: F = ∫02exsinx1+x2dxIt is a complex integration hence, numerical method is used.…

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A: The integration by parts formula is,    ∫u v' =uv - ∫v u'

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A: I am attaching image so that you understand each and every step.

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A: We draw required connection between the pattern and formulas as below.

Q: 412 Evaluate the integral (x² + y² + z²) dz dy dx. SSS 000 412 SS S (x² + y² + z²) dz dy dx = [ 000…

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Q: π I Find the volume of the region bounded above by the surface z = 7 sin x cos y and below by the…

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Q: The Area bounded by the parabola ay=x^2, the x-axis, and the line x=b is revolved about the x-axis,…

A: Given, Parabola- y=f(x)=x²/a Line- x=b Revolved about x-axis

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Q: 4. f(x) = 1-x 2x²-5x-3

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 3) Σ

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Q: find the equation of the tangent line to the graph of f(x)=x^2(x^1/2 +1) at x=4

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A: Let's find inverse laplace 9f given function.

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Q: 32) Find the amount of a continuous money flow in which $2000 per year is being invested at 5%,…

A: Given.

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A: Using formula of area of circle

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A: Topic = Integration

Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: 6. Find the area bounded by the curve y = log x, the x-axis, and the line x = 2.

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Q: Example 99 Consider the set M = {(x, y) = R²: x,y #0}. Find M. Solution:

A: The orthogonal complement are subspace

Q: Find the volume of the region bounded above by the paraboloid z = 3x² + 4y² and below by the square…

A: The region bounded above the z=3x2+4y2 and below by the region -3≤x≤3, -3≤y≤3

Q: 8 34) 2xe-x² dx <80 A) Convergent B) Divergent

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A: The objective is to evaluate the limit.

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Q: What is the slope of the line tangent to the polar curve r = ㅠ Ө - ? O 1 √√3 ✓ 2 T -||♡33 √√3 cos at…

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Q: 5. If f f(x) dx = 12 and f f(x) dx = 4, then all of the following must be true a. f f(x) dx = 16 ✓…

A: topic- definite integral

Q: 7 13 8 a Find the area of the shaded region above.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

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