Problem Set (Evaluating Definite Integrals)
For questions 1-9, evaluate the definite integrals:
(
Ans: 130
( ˆ ‰
Ans:
( Œ
Ans: 0.5
1.
2
3.
•
( a sin b
4.
Ans:
5.
(
csc ab
Ans: 1/4
( a b
6.
Ans: 3/55
( È
7.
use 2 decimal places
Ans: 14.36
8.
( È
9.
( ˆ 5‰
Ans: 8
Ans: 620.133
10.
A car's speed is given by where
where is hours and is miles/hour.
a) How far does the car travel in the 5 hours?
Ans: 166.7 miles
b) What is the average speed of the car?
Ans: 33.3 mph
Some Detailed Solutions
3.
I will use the property that ' ab ' ab
( Œ
( ˆ ‰
•
• •
Œ •
5.
To evaluate (
csc ab, let
csc ab (
csc ab
(
csc ab
(
cotab
cotab
•
•
cota b cota b
cotab cotab
To evaluate ( a b , let
6.
Then ( a b
(
•
•
8.
To evaluate (
, let
È
(
(
( È
È • ŠÈ È‹
a b
To evaluate ( ˆ 5‰ let
9.
( 5‰
ˆ
(
(
ˆ ‰ •
ˆ ‰
a) The distance traveled is ( ˆ ‰
10.
•
miles
miles
b) Average speed is equal to
5 hours
miles per hour.
0
