Without the screenshot, it's fairly difficult to know what your teacher wants exactly. I found this similar problem
brainly.com/question/13583475
which might help. It sounds like you have 4 semicircles which can be thought of as a division problem 12/3 = 4. Note how I'm dividing by 3 which is the width of each section (eg: from 6 to 9 is 9-6 = 3 units)
Answer: 1/30
Step-by-step explanation:
∫[0,4] arcsin(x/4) dx = 2π-4
x = 4sin(u)
arcsin(x/4) = arcsin(sin(u)) = u
dx = 4cos(u) du
∫[0,4] 4u cos(u) du
∫[0,4] f(x) dx = ∫[0,π/2] g(u) du
v = ∫[1,e] π(R^2-r^2) dx
where R=2 and r=lnx+1
v = ∫[1,e] π(4-(lnx + 1)^2) dx
Using shells dy
v = ∫[0,1] 2πrh dy
where r = y+1 and h=x-1=e^y-1
v = ∫[0,1] 2π(y+1)(e^y-1) dy
v = ∫[0,1] (x-x^2)^2 dx = 1/30
1,393.85 es la area de la pieza
