Suppose a function y = f(x) is so be revolved at x = e from point (a,b) to (c, d), what is the correct expression of the surface of revolution provided that the equation is continuous along the limits of integration? A. | 2mr(x)/T+[f"(x)]² dx 2m(x – e)/1+ [f'(x)]² dx c. 2nf(y)/1+[f']F dy D. 2n(e – x)/1 + [f'(x)]² dx

Q: Evaluate the integral (2x+3y) dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A: To Evaluate: I=∫C(2x+3y)dx+(6x-y)dy along the parabolic arc y=x2 from (0,0) to (1,1).

Q: Find the Particular Integral for the given differential equatiorn d²y dy +3- dx +6y =2x²+x+5 dx2…

A: using expansion,         (1+x)-1 =1-x+x2 -x3+...

Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy dx

A: Given: ∫-40∫x+42x+4siny3-3y2dydx To do: Evaluate the given double integral.

Q: Find a function f € span(1, cos x, sin x) which minimizes the integral 2πT √²* |x +1 − f(x)| ²dx.

A: Given a function                     f∈span1, cosx, sinx

Q: That the value of the integration g(1) = 00 , g(2) = 0 1-e t) -dt 9(t) where g is a function that is…

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Q: `s): The area of the surface obtained by rotating the curve y = ln(3x - 2), for 3 ≤ x ≤ e², about…

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Q: Find the differential of the function f(x,y)=x(e^-y) at (2,0). df=?

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Q: Evaluate the integral / (12x + 3y)dæ + (3x – y)dy along the parabolic arc y = x² from (0, 0) to (1,…

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Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

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Q: 4. Find the volume of the solid generated by the curve f(x)=4-cos.x revolved 360° about the x- axis…

A: Please check the region, given region is not bounded, we consider the region bounded by curve, x=0,…

Q: The integral that represents the arc-length of the curve y = In x, x E [2,3] is: A) 3 Vx2+1 dx. B)…

A: Please refer to the image below

Q: Verify directly from (3) that the solution has derivatives of all orders in {z > 0}. Asume that h(x,…

A: Sol

Q: Suppose the curve y = f(x) passes through the origin and the point (1,1). Find the value of the…

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Q: Evaluate the integration of the function. f(x) = 1+ e-x sinan over the fixed interval [a,b] = [0.1]…

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Q: Find the equation of the tangent plane to g ( x , y ) = e x cos ⁡ ( y )  at ( 0 , π ). Does g have a…

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Q: Evaluate the line integral (-3x+y)dx + (x + 3y)dy, where C lies along the x-axis from x = 0 to x = 6

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Q: 1 8y² = x² – x* , 5x< curve segment is %D - rotated about the x-axis. Calculate the surface area of…

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Q: px+y e- dt = xy %3| dy dx |(x,y)=(0,0) y satisfies the given integral. Find the derivative of y at…

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: To Determine: show that the differential forms in the integrals are exact. Then evaluate the…

Q: 2. Evaluate the double integral: Lo Sch sin (2³) VVT (Hint: Change the order of integration to dy…

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Q: 4. Supposea function y = f(x) is so be revokved at x = e from point (a, b) to (c, d), what is the…

A: Please refer the attached image for complete solution.

Q: If {(=)dz = f(x)dx f(x)dx + f(x)da f(x)dx, what are the bounds of integration for the first…

A: Solution:

Q: Solve the integral (5x - y)dx + (2x + cy)dy along the curves x = y3 from (0,0) to (1,1)

A: Explained below

Q: If 9. 3. 6. f(x)dx = || f(x)dz + 6. what are the bounds of integration for the first integral?…

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Q: 1. Sketch the region corresponding to the double integral rx+2 dy dx x2 and reverse the order of…

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: Evaluate the triple integral ∫ 2 to 0 ∫ 2x to 0   ∫ ln x to 0 xe^−y dy dx dz

A: The given integral can be written as: I=∫20∫2x0∫lnx0xe-ydydxdz…

Q: 6) Find the length of the arc of the curve y² =x ³ from (1, 1) to (2, 2 v2) twice using two…

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Q: Determine the total differential (dg), and total derivative with respect to x 3x 2y f(x, y, z) =…

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Q: Show that u (X ) = 3X+ 2x is asolution to the integral equation 3(1+x)? X - S sinh (x-t) ultJ dt

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Q: 15. Express c9-x² f(x, y)dy dx as an iterated integral in the or- der dx dy.

A: first, we will write an equation we have  y=0,y=9-x2x=-3,x=3 changing it w.r.t x we have…

Q: Let L be the length of the curve y = ln x from (1, 0) to (e,1). (a) Integrating with respect to x,…

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Q: 1- f(x, y) dy dx •x+1 f(x, y) dy dx + at is the sum of the four resulting limits of integration? 3.

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Q: 3. ( ) The integral f S, sin(y²)dydr cannot be evaluated since f sin(y³)dy is not an elementary…

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Q: Evaluate the integral (6x +12y)dx + (6æ — y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: Let us evaluate the given integral in the next steps.

Q: Verify the condition of integrability for the given total differential equatior (3x*y2 – e*z)dx +…

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Q: Evaluate the integral (8x +9y)dx + (3x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: We can observe that x is ranging from 0 to 1. We have the following. So,…

Q: 5. Compute the volume of the solid obtained by revolving the curve y = vx sin x about the x-axis…

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Q: find the general selution of the differential equetion by the fimear methodi sxy'-2y=x

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Q: Can you help me step by step?

A: dA/dt may be written as,

Q: 3 3 sin(x²) dx dy y by reversing the order of integration. With order reversed, I sin(x?) dy dx,…

A: Given:  Let I=∫03∫y3sinx2 dx dy To Find:  To evaluate the given integral by reversing the order of…

Q: 2.a) Apply the Trapezoid and corrected trapezoid rule, with h = 1, to approximate the integral 1 dx…

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Q: The integral that represents the arc-length of the curve y = In x, xE [2,3] is: %3D 3 x2+1 dx. Vx2+1…

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Q: Set up an integral that represents the length of the curve. = sin²(t), y = 1 –- 3 sin(t), 0 <t < T…

A: The given problem is solved below.

Q: From an integral equation corresponding to the diffrential equation d'y +x + y = 0 with the initial…

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Q: e for (2x + 1) cos(x) dx. 14. Use integration by parts to evaluate

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Q: dx dy Cvaluate the iterated integral: 1+ xy

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Q: Find the area between the curves y=e−0.2xy=e-0.2x and y=1.6x+1y=1.6x+1 from x=0x=0 to x=4x=4.

A: Given query is to find the area under the curve

Q: (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y =…

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Q: Find the differential dy of the function y=(cos(x))(7x) a. dy=-7x(sin(7x))dx b. dy=(-cos(x))(7x)dx…

A: To Find the differential dy of the function y=(cos(x))(7x)

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.