Find the area of the surface generated when the given curve is revolved about the y-axis. y= (3x/3, for sxs 64 3 O A. (257/2 -2°/2) O B. (257/2 -29/2) 3 Oc. (257/2-2/2) TC O D. (257 /2 -1)

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A: Given curve is y=14x2-12ln(x) Differentiate with respect to x. dydx=x2-12x

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A: Solve the given

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Q: r(t)=(cost+t sint)i+(sint -t cost)j, a/2<15a. %3D

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Q: Find the area of the surface obtained by revolving the given curve about the x-axis. on (0, In(3)

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Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

A: Given   Area of surface area revolved about x axis formula is

Q: a)Find the exact length L of the curve 3y? = (4x – 3)°, 1 0. Answer: b) Evaluate Sxe*dx Answer: 1 c)…

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Q: Find the arc length of the indicated portion of the curve given by r(t)= 2r°i+11r'j+10r'k, -1<t52

A: Solve the following

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A: Using area formula we have

Q: Find the surface area generated by rotating the semi-circle x = 49 – y? be- tween -7 < y 7 about the…

A: Given, x=49-y2  between -7≤y≤7 dxdy=1249-y2-2y=-y49-y2 By the formula:  S=∫2πx1+dxdy2 Plug the…

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A: Explanation of the solution is given below...

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y=x3 + for…

A: surface area of the curve is given by  S=2π∫abf(x) (f'(x))^2+1 dx

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A: Given:

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Q: Use the change in variables s = x + 4y, t = y to find the area of the ellipse x^2 + 8xy + 17y^2,…

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

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = =x² - 1 1,2…

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Q: Find the arclength of the curve x = 8t – 8, y = 15t +7 with 1 < t< 6.

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Q: Find the length of the curve C defined parametrically by C: r(t) = y(t) = e' sin t, 0<t<n e cost,…

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Q: The surface generated by revolving the curve c(t) = (t2, t) about the x-axis for 0 ≤ t ≤ 1.

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