Question

22. find the area of the surface generated by revolving the parametric curve about the y-axis.

x = 2 sin t + 1 , y = 2 cos t + 5 , (0) less than or equal to (t) less than or equal to (pi/4)

Answer 1

we know that area of the surface generated by revolving the parametric curve about the y-axis is given by,

where,

As t ranges from t = 0 to t = pi/4 we can say that,

-------------------------------------------1)

we have x = 2sin(t) + 1 hence,

we have y = 2cos(t) + 5 hence,

we have,

Hence,

we have,

Put them in equation 1) we can write,

we can write,

In decimal we can say that,

rounding to two decimal places we can say that,