See the attached file for questioins
Thehonest
calculus_review.docCalculus Review
1. An athlete exercises in a gym by pulling a spring. The force exerted by the spring at a distance x meters is 20x Newtons. The athlete pulls the spring a distance of 1 meter and repeats this 100 times. How much work does he do in one set? (You can neglect the work done returning the spring to its original position.)
2. Consider the graph of the function 1 + sin(x) between 0 and 2π. What is the volume of revolution created when the area under the graph is revolved around the y-axis?
3.
Consider the graph of the function
f x( ) = 1 9x + x3
fx
()
=
1
9x+x
3
between the points 2 and 5. What is the volume of revolution created when the graph is rotated around the y-axis?4. Find the anti-derivative of
x x2 + 2x + 2∫ dx
x
x
2
+2x+2
ò
dx
5.
Let
an = 1 4n
a
n
=
1
4
n
. Express the partial sum
Sn ≡ an n=1
N
∑
S
n
ºa
n
n=1
N
å
6. Integrate
ex sinx + cosx( )dx∫
e
x
sinx+cosx
()
dx
ò
