Determine Whether Each Integral Is Convergent or Divergent $\int _ { 0 } ^ { 2 } \frac { 1 } { x - 1 } d x$

question 228

Essay

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.(a) $\int _ { 0 } ^ { 2 } \frac { 1 } { x - 1 } d x$ (b) $\int _ { 2 } ^ { \infty } \frac { 1 } { x ( \ln x ) ^ { 2 } } d x$ (c) $\int _ { 0 } ^ { 1 } \frac { \ln x } { \sqrt { x } } d x$

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Definitions:

Median

The middle value in a data set, which divides the set into two equal halves when the values are arranged in ascending order.

IQR

The Interquartile Range, which measures the spread of the middle 50% of a data set.

Range

The difference between the highest and lowest scores in a set of data.

Median

The middle value in a dataset, dividing it into two equal parts when the data is arranged in ascending or descending order.