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Question: \(\int _ { 1 } ^ { 2 } \frac { d x } { x ^ { 2 } - 5 x + 4 } d x\) is...

∫12dxx2−5x+4dx\int _ { 1 } ^ { 2 } \frac { d x } { x ^ { 2 } - 5 x + 4 } d x is

A

Convergent and equal to 13log⁡2\frac { 1 } { 3 } \log 2

B

Convergent and equal to 3/log2

C

Divergent

D

None of these

Answer

Divergent

Explanation

Solution

13∫12(1x−4−1x−1)dx\frac { 1 } { 3 } \int _ { 1 } ^ { 2 } \left( \frac { 1 } { x - 4 } - \frac { 1 } { x - 1 } \right) d x =

13[log⁡2−∞]=−∞\frac { 1 } { 3 } [ \log 2 - \infty ] = - \infty

So the given integral is not convergent.