Algebra Equations Worksheets With Answer Keys Page 12
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1
2
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17
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20Chapter 5
12
1
=
6. Let
f x
( )
.
−
2
4
x
∫
(a) Determine
f x dx
( )
⎛ ⎞
x
⎛ ⎞
x
∫
∫
=
+
=
f x dx
( )
arcsin
C
+1
f x dx
( )
arcsin
⎜ ⎟
⎜ ⎟
⎝ ⎠
2
⎝ ⎠
2
+1 constant of integration
(b) What is the area of the region bounded by f , the x-axis, the y-axis,
x = ?
and the line
1
1
1
⎛ ⎞
1
∫
( )
∫
=
−
f x dx
( )
arcsin
arcsin 0
+1
f x dx
( )
⎜ ⎟
⎝ ⎠
2
0
0
π
+1 Fundamental Theorem of
=
Calculus
6
π
≈
0.524
≈
+1
0.524
6
(c) Determine the value of a that makes the following equality true:
a
π
a
∫
=
−
+1
f x dx
( )
arcsin
a
1
2
6
∫
∫
=
f x dx
( )
f x
( )
.
1
π
a
1
0
=
+1 arcsin
a
1
a
a
1
2
3
∫
∫
∫
=
−
=
f x dx
( )
arcsin
arcsin
f x dx
( )
f x
( )
π
a
⎛ ⎞
2
2
=
+1
sin
⎜ ⎟
1
0
1
2
⎝ ⎠
3
π
π
π
a
a
=
−
−
=
arcsin
arcsin
+1
3
2
6
6
2
6
π
a
=
arcsin
2
3
π
a
⎛ ⎞
=
sin
⎜ ⎟
2
⎝ ⎠
3
π
⎛ ⎞
=
a
2 sin
⎜ ⎟
⎝ ⎠
3
⎛
⎞
3
= ⎜
2
⎟
2
⎝
⎠
=
3
≈
1.732
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