Question from http://www.sgforums.com/forums/2297/topics/341192
O is the origin and A is the point on the curve y = tan x where x = π/3
i) Calculate the area of the region R enclosed by the arc OA, x-axis and the line x = π/3
ii)The region S is enclosed by the arc OA, the y-axis and the line y=√3.
Find the volume of the solid of revolution formed when S is rotates through 2π rad about the x-axis, giving answers in exact form.
iii) Find
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Answer:
i)
Point A = (π/3, √3)
Area of region R
= ln 2
= 0.693 units²
ii)
Rotate around x-axis (which is y=0 line)
So, volume = volume of cylinder - volume rotated under curve OA around x-axis
iii)
We can take the difference between the area of rectangle formed by x-axis, y-axis, x = π/3 and y = √3, and the area of region R.
Thus,
= ( π/3 )(√3) - 0.693
= 1.12 units²
