MCQ
The value of $\int\limits_0^2 {\frac{{dx}}{{{{(1 - x)}^2}}}} $ is
- A$-2$
- B$0$
- C$15$
- ✓indeterminate
✓
Answer
Correct option: D.
indeterminate
d
$\int\limits_0^2 {\frac{{dx}}{{{{(1 - x)}^2}}}} $ $= \int\limits_0^{{1^ - }} {\frac{{dx}}{{{{(1 - x)}^2}}}} \,\, + \,\,\int\limits_{{1^ + }}^2 {\frac{{dx}}{{{{(1 - x)}^2}}}} \,$
$\int\limits_0^2 {\frac{{dx}}{{{{(1 - x)}^2}}}} $ $= \int\limits_0^{{1^ - }} {\frac{{dx}}{{{{(1 - x)}^2}}}} \,\, + \,\,\int\limits_{{1^ + }}^2 {\frac{{dx}}{{{{(1 - x)}^2}}}} \,$
$= \left. {\frac{1}{{1 - x}}} \right]_0^{{1^ - }}\,\, + \,\,\left. {\frac{1}{{1 - x}}} \right]_{{1^ + }}^2$
$= (\infty - 1) + (-1) - (- \infty ) \Rightarrow$ indeterminant
Note that the shaded area is divergent 
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