Question

1.The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(e^x) is rotated about the x-axis. What is the volume of the generated solid?
a: 0.906 b:0.795 c:2.846 d: 2.498
2.Find the average value of f(x)=2/x over the interval [1, 3].
a: 1.10 b:2.20 c:0.55 d:0.33
3:For an object whose velocity in ft/sec is given by v(t) = −2t^2 + 4, what is its distance travelled, in feet, on the interval t = 0 to t = 2 secs?
a:4.876 b:2.667 c:9.752 d:2.438

Answer 1

#1
v = ∫[0,lnπ] π sin^2(e^x) dx
That will take some numerical methods to figure.

#2
∫[1,3] 2/x dx
-----------------
3-1

#3
s(t) = ∫[0,2] -2t^2+4 dt