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Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: A membranc of uniform density area is stracthed on a Circular frame of radius A to uniform stress…

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Q: The exact value of the integral [In[I + x) x²]+ 2dx is-0.3521. Evaluated this integral (a) by the…

A: (a)∫12x-x2+lnx+1+2 dx using n=4 trapezoids.The trapezoidal rule states…

Q: find fue area oy region R enclosed by Curves yexs and y=X= please Show yor working

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Q: Sketch the region enclosed by the curves and find its area. 1 х — 0, у — 1, у — е NOTE: Enter the…

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Q: By using double inpegrals, Find Ihe area the enclosed by of region b) cur ve x:- yo, Line e) curve…

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Q: sketch the regions bounded by z=0.67 and z=1.56 and find its area. show your solution in your paper

A: The standard normal distribution is a bell shaped distribution which is centred at the mean 0. The…

Q: Let fex) = %3D a) Find Xo tangent lir (Xo , f(Xo) b) Find the in a).

A: f(x)=kx2+C Tangent lines to the graph at (x0,f(x0)) and (-x0,f(-x0)) we know that when the tangent…

Q: 1 Evaluate f - dz over the unit circle in counter-clockwise direction using the parametriza- tions

A: To evaluate, ∮1zdz over the unit circle counter-clockwise

Q: Find the arc length of f(x) = In(cos x) on- %3D 4

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Q: A- Use Simpson's Rule with n=2 subintervals, evaluate the integral - Inx.dx, and compare the…

A: According to Simpsons rule, ∫abfxdx can be approximated to ∆x3fx0+4fx1+2fx2+4fx3+ ……

Q: what is the avorago valus OF a Funckon F on an Posterval [a,b]? 13 the given by vallis of Fa)-tan X,…

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Q: Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) trapezoidal rule, (4) parabolic…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: Why does in some cases, the arc length is changed to its parametric form to determine the line…

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Q: Calculate the arc length of y = x² – In(x) over the interval [1, 6e]. (Use decimal notation. Give…

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Q: With its curve y = cos determine its area under one arch.

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Q: Calculate the area of the intersection of the regions limited by curves r = 1 and r = 2(1 − cosθ).

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Q: The area under the region bounded by the curve f(r) cos r, the a-ax and the lines x = %3D and a = 2…

A: From the given curves the bounded region is as shown below: Now taking the vertical strip, so the…

Q: Let C be the curve given by f(x) = cosh x for 0 ≤ x ≤ t, where t &gt; 0. Show that the arc length of…

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Q: Approximate using the Trapezoidal rule with n = 4 subinte Round to 4 decimal places. sin r dr

A: See the details solution in below

Q: 4. у%3D 2х—х2, y = 2x² – 4x

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Q: A particular curve has unit binormal b - sin t, cos t, 2), unit normal n (- cost, - sin t, 0) and =…

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Q: Q: Prove that the arc lenfth af Curve y = log secx from to n- 3 is Use formula Note I+ ( dn.

A: Given: y = log sec x To prove: The arc length of the function y from x = 0 to is .

Q: Find an eqeation of the to the cune at the onuen povnt tangent line t 48) y=In(x²_ 7), (2,5)

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Q: Find the area bounded by axes and line 7x + 5y = 35 using any differential strip

A: Explained  below...

Q: 6 Find the center of mass of a thin plate of constant density & covering the region in the first and…

A: Calculate center of mass for x coordinate: x=∫x=01∫y=-61+x261+x2xdydx∫x=01∫y=-61+x261+x2dydx…

Q: Find arc length of vactor  valued function r(t)=ti+4tj+3tk over(0,1)

A: r(t)=ti+4tj+3tk over(0,1)

Q: Which integral computes arc length of f(x) = x5/2 on [0, 1]? 1 49 -x' dx 1+ 4 - 1 | V1+ x° dx 1 1+…

A: We have to find the arc length

Q: Find the moment with respect to x 2a the area bounded by x y and x2 = 2ay.

A: Given area is bounded by x=y and x2=2ay.  To find: Moment with respect to x=2a.   From x=y We get…

Q: y = sin(x), y = 2x

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Q: 5. Find the area enclosed by the inner loop of the curve r = 1-3 sin 0

A: Area Between Functions With Integration: The interval of the inner loop of the given polar curve is…

Q: An area is bounded by the x^2+10y-1600 curve  and the -xaxis. Find the moment of inertia (in units4)…

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Q: Sketch the region enclosed by the given curves. y = 7 cos(2x), y 7-7 cos(2x), 0 sxs x/2

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Q: From Rogawski ET 2e section 8.1, exercise 13. Approximate the arc length of the curve y = x the…

A: Solve the following

Q: Evaluate the line integral a xds where C is one quarter of a circle (in the first quadrant) of…

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Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

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Q: A Proton of mass (md is moving with un initial velecity (v) Collicling wwith ahelium atom of mass ()…

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Q: Use the Composite Trapezoidal rule with h = approximate the improper integral 1 sin 2x dx to

A: Given,        ∫01sin2xx3dx=

Q: Sketch the region bounded by the given curves, then find its area. 1. у%3D х*, у%3D2х

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: A curve is drawn on a sphere of radius "a' and the principal normal at a point P makes an angle 0…

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Q: Find the center of the mass of a thin plate of constant density ô covering the region 3 bounded by…

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Q: Sketch the region enclosed by the given curves. y = 4 cos(5x), y = 4 – 4 cos(5x), 0sxS a/5

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Q: Find the area of the circular sec- tor having radius 3 ft and 0 = 7.2radians %3D

A: Formula:

Q: Sind the Partial derivadiVes of th Jiven fuctions with Ves Pect x(2-CoS 2y)

A: We have to find the partial derivatives.

Q: Sketch the region enclosed by the given curves andfind its area.   y =cos x , y= 2- cos x  , 0 ≤ x ≤…

A: Given: The region enclosed by the curves  : y=cos(x)y=2-cos(x)           0≤x≤2π We have to sketch…

Q: Sketch the region enclosed by the given curves. y = 8 cos(x), y = 8 - 8 cos(x), 0<x T

A: This question is related to area bounded by curves, We will use integration to solve it.

Q: Sketch the region enclosed by the curves and find its area. 3 x = 0, y = 1, y = e3 x = -, NOTE:…

A: Let's find.