Let C be the curve y = 5/T for 1.l

Q: Q. 3 The solid of revolution obtained by rotating the region under the curve y = f(x), a sx sb,…

A: Formula: uv'=uv'+vu' Formula: sin x'= cos x The given function is: f(x)=x sin x, 1≤x≤2 The surface…

Q: a) l . Find the length of the curve 20 y= x, 0sx<3 V5 Length= b)! !: Find the area of the surface…

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Q: Use the area shown in the figure to find the value of each integral. a) S S(x) dx: у-аxis Area = 0.6…

A: The value of each integral given the area over the given integral  ∫abf(x) dxFrom x=a  to 0 the area…

Q: Q No 2. Find the area of the region enclosed by the curves y? = 4x and y = 2x – 4 By integrating (a)…

A: Given: y2=4x……1y=2x-4……2   To find area of the region enclosed by above curve: (a) By integrating…

Q: Find the surface area of revolution about the y-axis of y = over the interval 0 < a < 2. Enter your…

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Q: The area of the region outside the curve r=2+2cos0 and inside the curve r=3 is given by which…

A: Intersection points between two curves; r = 2 + 2 cos θ and r = 3 3 = 2 + 2 cos θ 1 = 2 cos θ cos θ…

Q: b) consider the area between the X-aXis and the curve y= Sin2x for Os X<#/2. when this area is…

A: Let's find.

Q: he region bounded by the curve = sin y- cos y 4 for 5л sys evolves about the y-axis 4 ee diagram).…

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Q: Ris the region bounded by the functions f(x) = 2 + Jz and the g(x) and the lines x=0 and x=4.…

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Q: 4. Evaluate the double integral: y f. L y¹/3 x7 +1 (Hint: Change the order of integration to dy dr.)…

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Q: Q4 Giving the following function fix.y), Sketch the region of integration and integrate fover this…

A: We are given  F(x,y)=1xy  over the square : 1≤x≤2 , 1≤y≤3  Required Integration  I=∫13∫12F(x,y) dx…

Q: Sketch the region whose area is represented by the definite integral. dx y 12 12 10- 10 8. 6 6 10 2…

A: The definite integral can be used to evaluate area of region bounded by curves. If over an interval…

Q: Q1) Find the average value of the area Ander the curve ( y= 1-x).

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: [1 + ytan(xy)]dx + x tan(xy)dy = 0 %3D

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Q: Find the moment of inertia with respect to a) x-axis, b) y-axis of the area in the first quadrant…

A: We will find out the required value.

Q: 1. Let the joint pdf of X and Y be given by fxy(r, y) = C exp + ry where C > 0 is an unknown…

A: Please note that as per our guidelines we can answer only the first three sub parts. Please post the…

Q: Q1) Find the average value of the area Ander the curve (y=1-x).

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the area between these two curves (use substitution method to solve integral) x = \yl V1 – y² &…

A: Explanation of the answer is as follows

Q: Q2 Using forward and backward difference approximations of O(h) and centered difference d²y…

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Q: Find the surface area generated by revolving about the y-axis that part of the curve y = In a lying…

A: The surface area of the curve y=fx, a≤x≤b, rotated about the y-axis is calculated by the following…

Q: Find the area enclosed by the curve x = t2 - 4t, y = -Vt and the y-axis. A = S rdy or A= S. (TR-IL)…

A: x=t2-4t, y=-ty=0 →t=0y=-2 →t=40≤t≤4dydt=-12t

Q: r6 Evaluate the integral dx dy by reversing the order of integration. NOTE: Enter the exact answer.…

A: We're going to solve

Q: Ris the region enclosed by the curves y= x³ +2, y= e=/2 – 2, z=2 and to the right of y-axis. Which…

A: To find the area of the region.

Q: The area of the region between the curve y = xr? – 6x +8 and the x-axis & r = 0 ; x = 3 is given by…

A: here option c is true because we will take the area in x -axis so will take limit of x and integrate…

Q: > Approximate o using the trapezoidal Rule x² dx Is this an wnderestmahon or over estimation ?

A: we have been given the function f(x)=x2

Q: Q2: Find the surface area generated by rotating for y = x² - ln(x) for x = [1, 2] about the y-axis.

A: We need to find Surface area.

Q: If m s f(x) s M for a s xs b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Consider the curve y = (1/2)x² from r = 0 to r = 1. (a) Write an integral for the arc length of this…

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Q: Evaluate the double integral I3 = SS (22-2 3) dxdy where S is the region in the 4th quadrant (y < 0,…

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Q: Sketch the region of integration and evaluate the integral. 1 y || 15y5 e xy dx dy ... Sketch the…

A: To sketch the region of integration and then solve the given integral.

Q: Evaluate the double integral: r2 Y To 0 √y¹/3 x7 +1 (Hint: Change the order of integration to dy…

A:

Q: r20 Evaluate the integral c5 dx dy by reversing the order of integration. NOTE: Enter the exact…

A: Double integration

Q: Set up an integral for the area of the surface generated by revolving the curve xy = 4 over 1 <y< 6…

A:

Q: Find the area of the region enclosed by the curve x=10cos(t)-5sin(2t) y=4sin(t) with 0<= t <=2pi

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Q: 3.6 Surface area = | f(x) dæ where 1.6 f( x ) = 3.6 Now integrate to find surface area = dx = 1.6

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Q: Quèstion 10 Find the shaded area under the curve. X~Normal(u = 50,0 = 8) 37.2 62.8 0.8384 O 0.8064…

A: We have given that,  X be the random variable from nirmal distribution with mean (μ) = 50 and…

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: We need to evaluate integral using Green's theorem.

Q: c) Calculate the flux. with respect to the outer normal, of F through the boundary lof the region…

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Q: Jy sinh dy

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Q: Evaluate dy dx by changing the order of x Vx4 + y? integration. Sketch the region of integration.

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Q: Let C be the curve y = 5/a for 1.8 < x < 3.3. 10 3 Find the surface area of revolution about the x-…

A: Given:

Q: Sketch the region of integration D and then change the order of integration from "dy dæ" into "dx…

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Q: 3.7 Surface area = dx where 1.2 f( x) = 3.7 Now integrate to find surface area = f(x) da = %3D 1.2

A: f(x)=3x

Q: Q8: Find the moment of inertia about the x & y axis for the area bounded by the curve y= e" and the…

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Q: Q2// Find the resulting volume of the curve y = sin x cos x rotation about the x-axis if x=0, x=/?

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Q: Find the value of the line integral. F. dr (Hint: If F is conservative, the integration may be…

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Q: C. Set-up the definite integral to find the length of the arc of the graph of y = Vx-1 from x = 2 to…

A: (C) Given the curve is y=x-1 and x=2,x=5. Find the arc length of the curve y=x-1 from x=2  to  x=5.…

Q: Q4. a) sketch the region of integration, reverse the order of integration, and evaluate the…

A: The given integral is ∫02∫04-x2xe2y4-ydydx. The objective is to integrate the given function by…

Q: ー元 Q.3 Sketch the region enclosed by the curves y = sec' x, y=x² +1, xr=- 4 and find 4. its area.

A: Sketch the region and integrate the function with x from -π/4 to π/4.