CEGEP CHAMPLAIN - ST. LAWRENCE
201-203-RE: Integral Calculus
Patrice Camiré
Arc Length
Find the arc length of the curve over the given x interval.
1. y = 3 + 2x3/2 , [0, 1]
2. y = 2(x + 3)3/2 , [0, 3]
3. y = ln(cos x) , [0, π/3]
4. y = ln(sec x) , [0, π/4]
5. y =
x3
1
+
, [1, 2]
3
4x
6. y =
x7
1
+
, [1, 2]
10 14x5
1
1
7. y = x2 − ln x , [1, 4]
2
4
8. y = ex , [0, 1]
Problem Sheet #15
Answers
2 √
1.
10 10 − 1
27
2.
√ 2 √
55 55 − 56 7
27
3. ln(2 +
4. ln(1 +
√
√
3)
2)
5.
59
24
6.
28603
2240
7.
1
(15 + ln 2)
2
8.
p
p
√
√
1 + e2 − 2 + ln( 1 + e2 − 1) − 1 − ln( 2 − 1)