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Mathematics
Mathematics
Problem
(i) Write the fraction
4
x
−
7
(
x
−
1
)
(
x
−
2
)
(
x
+
1
)
\frac{4x-7}{(x-1)(x-2)(x+1)}
(
x
−
1
)
(
x
−
2
)
(
x
+
1
)
4
x
−
7
as a sum of simple fractions whose denominators are the linear factors
(
x
−
1
)
,
(
x
−
2
)
(x-1),\,(x-2)
(
x
−
1
)
,
(
x
−
2
)
and
(
x
+
1
)
(x+1)
(
x
+
1
)
. (ii) Using the result of part (i) or otherwise, evaluate the definite integral
∫
3
5
4
x
−
7
(
x
−
1
)
(
x
−
2
)
(
x
+
1
)
d
x
.
\int_{3}^{5} \frac{4x-7}{(x-1)(x-2)(x+1)}\,dx.
∫
3
5
(
x
−
1
)
(
x
−
2
)
(
x
+
1
)
4
x
−
7
d
x
.
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