Integration (Chapter 15) 433
7aUse the identity cos^2 x=^12 +^12 cos(2x) to help evaluate
Z¼
4
0
cos^2 xdx.
b Use the identity sin^2 x=^12 ¡^12 cos(2x) to help evaluate
Z ¼
2
0
sin^2 xdx.
8 Evaluate the following integrals using area interpretation:
a
Z 3
0
f(x)dx b
Z 7
3
f(x)dx
c
Z 4
2
f(x)dx d
Z 7
0
f(x)dx
9 Evaluate the following integrals using area interpretation:
a
Z 4
0
f(x)dx b
Z 6
4
f(x)dx
c
Z 8
6
f(x)dx d
Z 8
0
f(x)dx
10 Write as a single integral:
a
Z 4
2
f(x)dx+
Z 7
4
f(x)dx b
Z 3
1
g(x)dx+
Z 8
3
g(x)dx+
Z 9
8
g(x)dx
11 a If
Z 3
1
f(x)dx=2 and
Z 6
1
f(x)dx=¡ 3 , find
Z 6
3
f(x)dx.
b If
Z 2
0
f(x)dx=5,
Z 6
4
f(x)dx=¡ 2 , and
Z 6
0
f(x)dx=7, find
Z 4
2
f(x)dx.
12 Given that
Z 1
¡ 1
f(x)dx=¡ 4 , determine the value of:
a
Z¡ 1
1
f(x)dx b
Z 1
¡ 1
(2 +f(x))dx c
Z 1
¡ 1
2 f(x)dx
d ksuch that
Z 1
¡ 1
kf(x)dx=7
13 If g(2) = 4 and g(3) = 5, calculate
Z 3
2
(g^0 (x)¡1)dx.
2
-2
2
4
y
6 x
y = f(x)
O
2
-2
2
4
y
68 x
y = f(x)
O
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Y:\HAESE\CAM4037\CamAdd_15\433CamAdd_15.cdr Monday, 7 April 2014 4:00:02 PM BRIAN