+91-9350504919 support@wiredfaculty.com
Wired Faculty Logo
Wired Faculty Logo Wired Faculty

Sponsor Area

Integrals

Question
CBSEENMA12032348
Wired Faculty App

Evaluate
integral subscript straight a superscript straight b straight x squared space dx  as the limit of sum.

Solution

Comparing integral subscript straight a superscript straight b straight x squared dx with integral subscript straight a superscript straight b straight f left parenthesis straight x right parenthesis space dx comma space space we space get comma
                          straight f left parenthesis straight x right parenthesis space equals space straight x squared
therefore                     straight f left parenthesis straight a right parenthesis space equals space straight a squared
               WiredFaculty
              .............................
         straight f left parenthesis straight a plus stack straight n minus 1 with bar on top minus straight h right parenthesis space equals space left parenthesis straight a plus stack straight n minus 1 with bar on top straight h right parenthesis squared
Now       integral subscript straight a superscript straight b space straight f left parenthesis straight x right parenthesis space dx space equals space Lt with straight h rightwards arrow 0 below space straight h left square bracket 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 right square bracket
where      nh space equals space straight b minus straight a
therefore          integral subscript straight a superscript straight b straight x squared dx space equals space Lt with straight h rightwards arrow 0 below straight h left square bracket straight a squared plus left parenthesis straight a plus straight h right parenthesis squared plus left parenthesis straight a plus 2 straight h right parenthesis squared plus.... plus left parenthesis straight a plus stack straight n minus 1 with bar on top straight h right parenthesis squared
         equals space Lt with straight h rightwards arrow 0 below space straight h left square bracket left parenthesis straight a squared plus straight a squared plus straight a squared plus..... space to space straight n space term right parenthesis space plus space 2 space straight a space straight h space left curly bracket 1 plus 2 plus 3 plus... plus stack straight n minus 1 with bar on top right curly bracket space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space
                                                                          plus straight h squared left curly bracket 1 squared plus 2 squared plus 3 squared plus.... plus left parenthesis straight n minus 1 right parenthesis squared right curly bracket right square bracket
WiredFaculty
WiredFaculty
equals space left parenthesis straight b minus straight a right parenthesis open square brackets fraction numerator 3 straight a squared plus 3 straight a left parenthesis straight b minus straight a right parenthesis plus left parenthesis straight b minus straight a right parenthesis squared over denominator 3 end fraction close square brackets
WiredFaculty

Some More Questions From Integrals Chapter

Sponsor Area

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation