Which is correct

Question

If , then 

3π.

5π.

6π.

8π.

Answer 1

6pi is the best answer

from 4 to 6 with f(x)=2pi

means the area under the curve is 2(2pi) = 4pi

that excludes 3pi as false

then there's an area = integral of square root of (16-x^2) evaluated between 0 and 4

which is a little more than a right triangle's area of 4(4)/2 = 8

8 = about 2.58(3.1459) =2.58pi

4pi + 2.58pi = 6.58pi and it's understated, which is a close call between 6pi and 8pi

integral of sqr(16-x^2) = (x/2)sqr(16-x^2) + 8arcsin(x/4) (use an integral table or integral calculator)

evaluate from 0 to 4 gives

0 + 8arcsin(4/4) -0 + 8arcsin(0/4)

= 8arcsin(1)

= 8(pi/2)

= 4pi

add the two areas together: 4pi to 4pi = 8pi

Answer 2

Calculus! I hope this helps... send more!

Frederick M.