Book Store

Download books and chapters from book store.
Currently only available for
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for
Class 10 Class 12

નિયત સંકલન

નીચે આપેલાં નિયત સંકલિતને સરવાળાના લક્ષ સ્વરૂપે મેળવો :

$integral from 1 to 3 of space open parentheses straight x squared space plus space straight x close parentheses space dx$

નીચે આપેલાં નિયત સંકલિતને સરવાળાના લક્ષ સ્વરૂપે મેળવો :
$integral from negative 1 to 1 of space straight e to the power of straight x space dx$

નીચે આપેલાં નિયત સંકલિતને સરવાળાના લક્ષ સ્વરૂપે મેળવો :
$integral from 0 to 1 of space straight e to the power of 2 minus 3 straight x end exponent space dx$

નીચે આપેલાં નિયત સંકલિતને સરવાળાના લક્ષ સ્વરૂપે મેળવો :
$integral from 1 to 2 of space 3 to the power of straight x space dx$

અહી, વિધેય f(x) = 3^x એ [1, 2] માં સતત છે.

[1, 2] નું સમાન લંબાઈના n ઉપાંતરાલોમાં વિભાજન કરતાં,

પ્રત્યેક ઉપાંતરાલની લંબાઈ $straight h space equals space fraction numerator straight b space minus space straight a over denominator straight n end fraction space equals space fraction numerator 2 space minus space 1 over denominator straight n end fraction space equals space 1 over straight n$ થશે.

તેથી nh = 1 મળે. તથા જેમ $straight n space rightwards arrow space infinity$ તેમ $straight h space rightwards arrow space 0$ થશે.

હવે, વ્યાખ્યા પ્રમાણે,

$integral from 1 to 2 of space 3 to the power of straight x space dx space equals space limit as straight h rightwards arrow 0 of space straight h space sum from straight i space equals space 1 to straight n of space straight f open parentheses 1 space plus space ih close parentheses space space space space open parentheses because space straight a space equals space 1 close parentheses$

$equals space limit as straight h rightwards arrow 0 of space straight h space sum from straight i space equals space 1 to straight n of space 3 to the power of 1 space plus space ih end exponent equals space limit as straight h rightwards arrow 0 of space straight h space sum from straight i space equals space 1 to straight n of space 3 space times space 3 to the power of ih equals space limit as straight h rightwards arrow 0 of space 3 straight h space sum from straight i space equals space 1 to straight n of space 3 to the power of ih equals space limit as straight h rightwards arrow 0 of space 3 straight h space open square brackets 3 to the power of straight h space plus space 3 to the power of 2 straight h end exponent space plus space 3 to the power of 3 straight h end exponent space plus space........ space plus space 3 to the power of nh close square brackets equals space limit as straight h rightwards arrow 0 of space open square brackets fraction numerator 3 straight h space times space 3 to the power of straight h space open parentheses 3 to the power of nh space minus space 1 close parentheses over denominator 3 to the power of straight h space minus space 1 end fraction close square brackets space space space space open parentheses because space straight S subscript straight n space equals space fraction numerator straight a open parentheses straight r to the power of straight n space minus space 1 close parentheses over denominator straight r space minus space 1 end fraction space semicolon space straight r space not equal to space 1 close parentheses equals space limit as straight h rightwards arrow 0 of space open square brackets 3 space times space fraction numerator 1 over denominator begin display style fraction numerator 3 to the power of straight h space minus space 1 over denominator straight h end fraction end style end fraction space times space 3 to the power of straight h space open parentheses 3 to the power of 1 space minus space 1 close parentheses close square brackets space space space space open parentheses because space nh space equals space 1 close parentheses$

$equals space 6 space times space fraction numerator 1 over denominator log subscript straight e space 3 end fraction space times space 3 to the power of 0 space equals space fraction numerator 6 over denominator log subscript straight e space 3 end fraction space equals bold space bold 6 bold space bold log subscript bold 3 bold space bold e$

નીચે આપેલાં નિયત સંકલિતને સરવાળાના લક્ષ સ્વરૂપે મેળવો :
$integral from log subscript straight e space 2 to log subscript straight e space 5 of space straight e to the power of straight x space dx$

Switch

Chapter Chosen

Book Chosen

Subject Chosen

Book Store

Previous Year Papers

નિયત સંકલન

Switch