5. a) Set up, but do not evaluate, an integral for the surface area of the object obtained by rotating y = sin(2x),0 ≤ x ≤ about the x-axis using, i) ds = ii) ds = + dx dx dy dx dy b) Find the surface area of the object obtained by rotating y = 4-x, 1 ≤x≤6 about the y-axis.

Q: B7. Refer to the shaded object in Figure QB7, y = -2x² +2 Part B: Determine: 1 y a) the area for…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: The area of the surface obtained by rotating the curve y = x2, 0sxs1 about the y-axis is

A:

Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √√x, 1 ≤ y ≤2

A: Given y=x13    1≤y≤2Rotating about y-axisarea of surface of revolution about tghe y…

Q: Find the surface area for the object obtained by rotating y=7x+2 about the x-axis over the interval…

A:

Q: What is the area of the enclosed surface bounded by the x-axis, x = 2 and y=x2 ?

A: The area under the curve can be calculated by the integration. The formula for the integration is…

Q: Find the area of the surface of the solid formed by revolving one arch of the parametric curve given…

A:

Q: 3. Find the area of the cardioids region shared by ri 7(1- sin 0) and r2 = 7(1+sin 0). A 7(1 Sint) B…

A: The given curves are:  r1=71-sinθr2=71+sinθ To find the intersecting points,…

Q: Find the area of the surface obtained by rotating the curve y = √5x from x = 0 to = 4 about the…

A:

Q: Consider the curves x = 12y? and x + 6y = 18. a) Determine their points of intersection (x1, Y1) and…

A: Given :   x=12y2 x+6y=18

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y? = 4(x² –…

A: Given: y2=4x2-a2 Portion of the curve in the 1st quadrant is revolved about x=0 (y-axis) from y=0 to…