Set up, but do not evaluate, the integral to find the area of the surface generated when the curve y = 3 sinx, defined on [0, π], is rotated about the x-axis. 67 f (sin x)(1+3 cos x) dx O6T- sin x fỏ* V1+9cos2 xda O fỏ" 2ar 1+3sinxde O 67 f (sin 2) V1+9 cos? ada

Q: 17. Evaluate the integral or show that it is divergent [(a)-(c)]. 4 6 14 dx (a) wzda, f (b) (b)dx,…

A: As per the instruction, we will be answering the first three subparts. For (a),…

Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1) b) has…

A: vector equation of line

Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: f(x)-f(a) a. Use the definition mtan = lim x-a x-a b. Determine an equation of the tangent line at…

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Q: Solve for the variable using a method of your choice. 72+7+72+6 7x+6= 8

A: The detailed solution is given below Thank you

Q: 3. Find the average value of the function on the given interval. a. f (x) = 4x − x², [0,3] 2 2 b. f…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: T/6 3 coss 3x dx

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Q: Use the method of elimination to evaluate the determinants

A: Question number 16 has been solved as per the request of the student.     This question can be…

Q: f(x) = x² + 5x - 1

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Q: Find the orthogonal trajectories of the given family of curves. 1. y = c (sec x + tan x )

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

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Q: Given x = y²+2y 8 -In(y + 1), find the arc length for 0 ≤ y ≤3

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Q: 4 The slope of the tangent line to the curve y = X at the point 5, is: 5

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Q: Let integral in the order of dadzdy, then what are the limits of integrations? A.0 sz55, Osys…

A: Concept: Changing the limits of the triple integral: A sequential triple integral can be presented…

Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

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Q: Find an equation of the tangent line to the given curve at the specified point. = (1, e) X y =

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Q: 6. f(In x)² dx

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Q: find the inverse Laplace Transform of the functions     a.) 5/3s b.)14/((3s+2)(s-4))

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Q: Text Canada's population is about 33 million people. It is increasing at about 1.8% per year. How…

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Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy +…

A: We have to find the general solution of the given differential equation using variation of…

Q: Solve the following differential equations: 2 √1-y² (a) - dx + y sin 2x -dy = 0 cos 4x+1

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Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x - 2).

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Q: Evaluation. Determine the antiderivative for each. Show complete solution 1. S dx 5x³-3 √x3 2.…

A: As we know that; The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1       1).…

Q: Find the slope of the tangent line to the graphof the polar equation 1 r = at Ø= 1-sinø 6

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Q: Ji 16 sin² x cos² x dx dx B

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Q: Solve f(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: Solved below.

Q: 4. Determine the number of terms in the sequence: -45, -32, -19, -6, 410 ***

A: There are 36 terms  in the sequence.

Q: If f is continuous on [0, 1], prove that f₁¹ f(x) dx = f₁¹ ƒ(1 − x)dx.

A: This question can be solved using properties of definite integrals.

Q: 3. The region bounded by the curve y=sec x, the x axis, the y axis and the line x=0.25pi is revolved…

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Q: Question 4 Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

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Q: z is a function of x and y implicitly defined by Find and i at (x, y, z) = (0, 2, -1) əz Əx Əy y³…

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Q: Find the length of the curve. Hand written plzz √2ti + ej+ek, 0 ≤t≤ 3

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Q: 2. If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 23rd…

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Q: 1. u= x² + y² + z²

A: On solving this we will get

Q: 7) x¹ 9-x ² dx X 3 2 2 where u-x ² dv = x √ 9-x² dx 2

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Q: Find the volume of the solid generated by the region bounded by x² + y = 6, y = x, y = -2 and x = -2…

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Q: Write as a single function of a single angle. tan 55° - tan 17⁰ 1+tan 55° -tan 17° = [? ] ([_]°)

A: Use the formula of tan(A-B)

Q: Question

A: Please refer to the image below

Q: Let S be the surface with equation (z - 4)² = 4x² + 4y². Viewing S as a surface of revolution, find…

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Q: 2. If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 23rd…

A: Topic = Sequence

Q: 2. Evaluate 3 dx -) S (x+5)(2-3)dx, (b), (c)²-22²-da, J ■) x³ −2x² −4 −1+ int: (c) 1 + ² + ²/1/2 x³…

A: Topic:- application of integration

Q: ƒ(x)=3x² +6x−9

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Q: Ex: If w cos(uv), u = = xyz, y = π 4(x²+y²)' aw find at point (1, 1, 1). əx

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Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

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Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

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Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

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Q: 2. Given: polar curves C₁ : r = √√√2- cos 0 and C₂ : r = √√√2 + sin intersecting at A(³√2, ³) and…

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Q: Find the area bounded by the curves y-x² = -3,x+y = 3 and y = 0.5x.

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Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

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Q: A product can be produced at a total cost of C(x) = 500 + 100x² + x³ dollars, where x is the number…

A: Solved below.