Q2. Let f(x)= In(cos x) (i) Find the arc length (ds) of the function (ii) Determine the surface area of the solid obtained by rotating the function over the interval 0sxs", about the x-axis. 4

Q: Indepen-dent Variable Depen-dent Variable Equation Order Degree z(iv) + z" = -y y' + ay = bt f" + f'…

A: We have to identify the independent variable , dependent variable, order and degree of the given…

Q: Compute the surface area of the surface generated by revolving the curve c(t) = (t, e') about the…

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Q: x = 2 sin-1 1, y = In (1 – r²) (0<1s!)

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Q: The longest interval in which the 1.V.P y" +(tanx)y- xy = x, y(1) = 3, y'(1) =0 surlay has a…

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Q: The arc length of y = 5++ from x = 1 to x : 2x (A) f 1+ (5 ++² dx +2 dx 2x (B) 2x2 (C) f1+ x2 dx 2x2…

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Q: Find the work done by F = 2xy°i + 7x²y²j in moving a particle once counterclockwise around the curve…

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Q: Find the equation of the tangent plane to the surface determined by z'y' + z – 25 = 0 at z = 4, y =…

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Q: y = 3x² – 1 from x = 0 to x = 1 . 3. Find the exact arc length of the curve

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Q: I = (4xy' + (y')²)dx

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Q: Find the tangent plane to the surface f(x, y) = e" cos y +e*sin y at (-1, ;). %3D OAz=-e(z+…

A: Option A is correct option.

Q: Q3. a. Evaluate the line integral e xey ds, where C is the line segment from (-1,2) to (1,1) and ds…

A: Evaluate the line integral ∫Cxexds, where C is the line segment from (−1,2) to (1,1 ) and ds is the…

Q: (x² + y?)3/2' + (x² + y?)3/2J OVer the curve F(t) = (e' cos(t))i+ (e' sin(t))j from the point (1,0)…

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Q: State the characteristics (type, order, degree) y y" - V1+ (y')² = 0

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Q: The longest interval in which the 1.V.P y"+(tanx)y-xy = x, y(1) = 3, y'(1) =0 surlay has a solution…

A: Given differential equation is. y''+tanxy'-xy=x The initial condition as, y1=3,  y'1=0 On comparing…

Q: The longest interval in which the 1.V.P y"+(tanx)y- xy = x, y(1) = 3, y'(1) = 0 surlay has a…

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Q: A thin wire has the shape of the curve C traced by r(t) = cos(nt)i + tj+ (sin(nt) + 5)k. 0 st<1 (a)…

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