2.) Find the exact area of the surface obtained by rotating the curve about the x-axis y= cos(÷x) 0 < I

Q: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y = 2r² (0 <t s…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + ex,…

A:

Q: cos(3t), y = 6+ sin(3t) on 0 <t <

A: Please see the explanation below

Q: Find the area of the surface generated by revolving the curve x= cos (3t), y = 5+ sin (3t) on 0sts,…

A: Suppose parametric curve rt=xt,yt for a≤t≤b are revolving about the x-axis then surface area…

Q: Find the area of the surface obtained by rotating the curve x = 6 cos 0, y = 6 sin³ 0, 0< 0 <n/2 %3D…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 2 + 2)3/2, 1s ys…

A: The curve x=13y2+232 revolved about x-axis on 1≤y≤4

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √ 1 + ex,…

A: We need to find Surface area.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x -(y2 + 2)3/2,…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 2 + 4y2,…

A: To find the exact area of the surface obtained by rotating the curve about the x-axis. x=2+4y2    ,…

Q: Find the areas of the surfaces generated by revolving the curves about the indicated axes.x = cos t,…

A:

Q: (b) Use Simpson's Rule with n = 10 to estimate the area of the surface obtained by rotating the sine…

A: Let's solve area of surface.

Q: 3. Find the area of the surface generated from revolving the curve y =x ++4 from x = 1 to x = 2…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 y = + /- 2x

A: Given: The equation of the curve y=x36+12x,where  12≤x≤1. Calculation: Compute the surface area as…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + ex, 0<…

A:

Q: cos(2t), y = 4+ sin(2t) 0 <t< on 2

A:

Q: Find the area of the surface generated by revolving the curve about the given axis. x = 2 cos(0), y…

A:

Q: Find the area of the surface obtained by rotating the curve y = cos 2x, x is an element of  [ 0,…

A:

Q: Find the area of the surface generated by revolving the given curve about the x- axis: y = 19 – x²,…

A: Given,y=9-x2   squaring both the sides,y2=9-x2x2+y2=9x2+y2=32this is the equation of the circle with…

Q: Find the area of the surface generated by revolving the curve x = 2 cos θ,       y = 2 sin θ,   0 ≤…

A: If x=f(t), y=f(t) then surface area is, About x axis: S=2π∫abydxdt2+dydt2dt About y axis:…

Q: 1. a) Find the length of the curve: y=+[1,2]. b) Find the area of the surface obtained by rotating…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √ 1 + ex,…

A:

Q: Find the exact area of the surface obtained by rotatingthe curve about the x-axis. y =√(1+ ex)  ,…

A: Given: y=1+ex , 0≤x≤1 The area of the curve is obtained by rotating the curve f(x) about x-axis…

Q: Find the area of the surface formed by revolving the circle r = f (0) cos 0 about the line θ = π/2.…

A:

Q: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

A:

Q: Find the area of the surface generated by revolving the curve about the given axis. x = 6 cos(e), y…

A: Solution

Q: 3. Find the area of the surface generated from revolving the curve y =x++ 4 from x 1 to x 2 about…

A: Given, Curve ,y=x33+14x+4 To find : Area of surface generated after revolving the given curve from…

Q: 36. Find the area of the surface generated by revolving the para- metric curve x = cos² 1, y = sin?…

A: Definition used -                               Area of the surface generated by revolving the…

Q: Find the area of the surface generated by revolving the given curve about the indicated axis. 1. x =…

A: Consider two parametric equations and with . Then the area of the surface obtained by rotating…

Q: Find the area of the surface generated by revolving about the y-axis the arc C given by C = { (x,y)…

A:

Q: 8.) Find the area of the surface by revolving the curve about each given axis. 1 x =t3, y = t + 1,…

A:

Q: Consider the curve y = 3 sin(2x), where 0 < x < n/2. Find the surface area when this curve is…

A: We have given the function; We know the formula for surface area by revolution;

Q: 5. Find the exact area of the surface obtained by rotating the curve y = V16 x2, -2<*<2 about the…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + ex,…

A: Given curve is y=1+ex and we have dydx=ex21+ex Since the Area of the surface obtained by rotating…

Q: 4. Find the area of surface that is generated by revolving the portion of the curve I = 2/1- y,…

A:

Q: 6. Find the exact area of the surface obtained by rotating the curve, y = x³, 0 < x < 2, about the…

A:

Q: y = cos(x), 0 <x<

A: Consider the given surface whose area is required to calculate.

Q: 8) Find the area of the surface generated by rotating about the x-axis the arc of the curve y x…

A:

Q: Find the area of the surface obtained by rotating the given curve about the x-axis. x=…

A: The area of the surface obtained by rotating the curve about x-axis is given by the formula…

Q: 13. Find the area of the surface generated when the curve = , on [2,4] is rotated about the y-axis.

A: The solution are next step is

Q: 3. Consider the surface sin (xy)+ cos (xz)+sin ( yz) =1. Find an equation for the tangent plane to…

A:

Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

Q: b) Sketch the graph and find the points on the cardioid r=a(1+cos) at which tangent lines are…

A: Consider the equation of the cardioid, r=a1+cosθ The graph will be,

Q: b-Two curves x = 0 – sin 0, y = 1 - cos 0 are rotated around the y-axis. Calculate the area of the…

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Q: x=y"2 -y², 1<y<3 about the y-axis 3°

A:

Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the xx-axis.  y=sin(πx/8),…

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Q: Consider the curve y = 3 sin(2x), where 0 < x < T/2. Find the surface area when this curve is…

A: To find the surface area when the curve the is rotated about the x-axis.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. < =v² + 2)3/2, 3…

A:

Q: 1. (a) Find the exact area of the surface obtained by rotating the curve y = e* about the x-axis…

A: