Due Tuesday, January 18th
Please don’t try to fit your answers onto this page. They won’t fit.
1. Find
Z
5 f ( x ) dx for the function
0 f ( x ) =

2 x, if 0 ≤ x ≤ 1


2 if 1 < x ≤ 2

 x if 2 < x ≤ 5
Hint: It might be easier to draw the graph and use geometry.
2. Compute the following integrals:
(a)
(b)
(c)
Z
8
| x
2 − 6 x + 8 | dx
0
Z cos(
1 t
) t 2 dt
Z sin x sec
2
(cos x ) dx
(d)
(e)
(f)
Z
8 √
3 y ( y − 1) dy
1
Z
4
− 4
16 − t
2
√
3
2 dt
Z
1 √
5 x 4 dx
0
3. For the following, sketch the region bounded by the graphs of the given equations, set up and integral and calculate the area of the region. Make an estimate of the area to confirm your answer.
(a) y = x , y = x
3
(b) x = (3 − y )( y + 1) , x = 0
√
(c) y = x − 1 , x − 3 y + 1 = 0
(d) x = 1 − y 2 , x = y 2 − 1
4. Find the number b such that the line y = b divides the region bounded by the curves y = x
2 and y = 4 into two regions of equal area.
5. An object moves along a line so that its velocity at time t is v ( t ) = 3 t
2 − 24 t + 36 feet per second. Find the displacement and total distance traveled by the object for − 1 ≤ t ≤ 9.