Question

Evaluate the following definite integral as limit of a sum.
$integral subscript 1 superscript 2 xdx$

Solution

Comparing $integral subscript 1 superscript 2 xdx space with space integral subscript straight a superscript straight b straight f left parenthesis straight x right parenthesis space dx comma space space we space get comma$
$WiredFaculty$
$therefore space space space space straight f left parenthesis straight a right parenthesis space equals space straight a comma space space straight f left parenthesis straight a plus straight h right parenthesis space equals space straight a plus straight h comma space space straight f left parenthesis straight a plus 2 straight h right parenthesis space equals space straight a plus 2 straight h comma space...... comma space straight f left parenthesis straight a plus stack straight n minus 1 with bar on top straight h right parenthesis space equals space straight a plus left parenthesis straight n minus 1 right parenthesis space straight h$
Now $integral subscript straight a superscript straight b straight f left parenthesis straight x right parenthesis space equals space Lt with straight h rightwards arrow 0 below space straight h open square brackets straight f left parenthesis straight a right parenthesis plus straight f left parenthesis straight a plus straight h right parenthesis plus straight f left parenthesis straight a plus 2 straight h right parenthesis plus... plus straight f left parenthesis straight a plus stack straight n minus 1 with bar on top straight h right parenthesis close square brackets$
$rightwards double arrow$ $integral subscript straight a superscript straight b xdx space equals space Lt with straight h rightwards arrow 0 below straight h space left square bracket straight a plus left parenthesis straight a plus straight h right parenthesis plus left parenthesis straight a plus 2 straight h right parenthesis plus... plus left parenthesis straight a plus stack straight n minus 1 with bar on top space straight h right parenthesis right square bracket$
$WiredFaculty$
$WiredFaculty$

For Daily Free Study Material Join wiredfaculty

WhatsApp Group

Download Android App

Ncert Book Download

Integrals

Evaluate the following definite integral as limit of a sum.
$integral subscript 1 superscript 2 xdx$

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location