Sponsor Area

Inverse Trigonometric Functions

Question
CBSEENMA12032620

Evaluate

open vertical bar table row cell straight x squared minus straight x plus 1 end cell cell space space space space space straight x minus 1 end cell row cell straight x plus 1 end cell cell space space space space straight x plus 1 end cell end table close vertical bar

Solution
Let space increment equals open vertical bar table row cell straight x squared minus straight x plus 1 end cell cell space space space space space straight x minus 1 end cell row cell straight x plus 1 end cell cell space space space space straight x plus 1 end cell end table close vertical bar equals left parenthesis straight x squared minus straight x plus 1 right parenthesis left parenthesis straight x plus 1 right parenthesis minus left parenthesis straight x minus 1 right parenthesis left parenthesis straight x plus 1 right parenthesis space
space space space space space space space space equals straight x cubed minus straight x squared plus straight x plus straight x squared minus straight x plus 1 minus straight x squared plus 1 equals negative straight x cubed minus straight x squared plus 2 space space

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