Evaluate the following integral as limit of a sum from Mathemat

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsLong Answer Type

11.

Evaluate integral subscript 0 superscript 2 left parenthesis straight x squared plus straight x plus 2 right parenthesis space dx as the limit of a sum.

102 Views

12.

Evaluate integral subscript 0 superscript 2 left parenthesis straight x squared plus straight x plus 1 right parenthesis space dx as the limit of a sum.

104 Views

13.

Evaluate  integral subscript 1 superscript 3 left parenthesis straight x squared plus straight x right parenthesis space dx as the limit of sums. 

188 Views

 Multiple Choice QuestionsShort Answer Type

14.

Evaluate integral subscript 1 superscript 2 left parenthesis straight x squared plus straight x right parenthesis dx as the limit of a sum.

102 Views

Advertisement
15.

Evaluate integral subscript 0 superscript 2 left parenthesis straight x squared plus straight x right parenthesis space dx as the limit of sum.

84 Views

 Multiple Choice QuestionsLong Answer Type

16.

Evaluate as limit of sums integral subscript 1 superscript 4 left parenthesis 5 straight x squared plus 3 straight x right parenthesis space dx.

86 Views

17.

Evaluate as limit of sums integral subscript 1 superscript 4 left parenthesis 3 straight x squared plus 2 straight x right parenthesis space dx.

92 Views

18.

Evaluate as limit of sums: integral subscript 1 superscript 3 left parenthesis 2 straight x squared plus 3 straight x right parenthesis space dx. space

179 Views

Advertisement
Advertisement

19. Evaluate the following integral as limit of a sum
integral subscript 0 superscript 2 left parenthesis straight x squared plus 3 right parenthesis space dx.


Comparing integral subscript 0 superscript 2 left parenthesis straight x squared plus 3 right parenthesis space dx space with space integral subscript straight a superscript straight b straight f left parenthesis straight x right parenthesis space dx comma we get,
                    straight f left parenthesis straight x right parenthesis space equals space straight x squared plus 3 comma space space straight a space equals space 0 comma space space straight b space equals space 2
straight f left parenthesis straight a right parenthesis space equals space straight f left parenthesis 0 right parenthesis space equals space 0 plus 3 space equals space 3
           straight f left parenthesis straight a plus straight h right parenthesis space equals space straight f left parenthesis 0 plus straight h right parenthesis space equals space straight f left parenthesis straight h right parenthesis space equals space straight h squared plus 3
straight f left parenthesis straight a plus 2 straight h right parenthesis space equals space straight f left parenthesis 0 plus 2 straight h right parenthesis space equals space straight f left parenthesis 2 straight h right parenthesis space equals space 2 squared. space straight h squared plus 3
....... 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.....

      straight f left parenthesis straight a plus stack straight n minus 1 with bar on top space straight h right parenthesis space equals space straight f left parenthesis stack straight n minus 1 with bar on top space straight h right parenthesis space equals space left parenthesis straight n minus 1 right parenthesis squared space straight h squared space plus space 3
Now   integral subscript straight a superscript straight b 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 space plus space straight f left parenthesis straight a plus straight h right parenthesis space plus space straight f left parenthesis straight a plus 2 straight h right parenthesis space plus... plus straight f left parenthesis straight a plus stack straight n minus 1 with bar on top space straight h right parenthesis
therefore      integral subscript 0 superscript 2 left parenthesis straight x squared plus 3 right parenthesis dx space equals space Lt with straight h rightwards arrow 0 below space straight h left square bracket 3 plus open curly brackets straight h squared plus 3 close curly brackets space plus open curly brackets 2 squared. space straight h squared space plus space 3 close curly brackets space plus space................
                                                                                            plus space open curly brackets left parenthesis straight n minus 1 right parenthesis squared. space straight h squared space plus space 3 close curly brackets right square bracket
                                 equals space Lt with straight h rightwards arrow 0 below space straight h open square brackets 3 space straight n space plus space straight h squared space open curly brackets 1 squared plus 2 squared plus 3 squared plus..... plus left parenthesis straight n minus 1 right parenthesis squared close curly brackets close square brackets
equals space Lt with straight h rightwards arrow 0 below space straight h open square brackets 3 space straight n space plus space straight h squared. space fraction numerator left parenthesis straight n minus 1 right parenthesis space left parenthesis straight n right parenthesis space left parenthesis 2 straight n minus 1 right parenthesis over denominator 6 end fraction close square brackets
space equals space Lt with straight h rightwards arrow 0 below open square brackets 3 left parenthesis straight n space straight h right parenthesis space plus space fraction numerator left parenthesis straight n space straight h right parenthesis space left parenthesis nh space minus straight h right parenthesis space left parenthesis space 2 space straight n space straight h space minus space straight h right parenthesis over denominator 6 end fraction close square brackets
                             equals space Lt with straight h space rightwards arrow 0 below space open square brackets 3 space left parenthesis 2 space right parenthesis plus space fraction numerator left parenthesis 2 right parenthesis space left parenthesis 2 minus straight h right parenthesis space left parenthesis 4 minus straight h right parenthesis over denominator 6 end fraction close square brackets space space space space left square bracket because space space straight n space straight h space equals space straight b minus straight a space equals space 2 minus 0 space equals space 2 right square bracket
                           equals space 3 left parenthesis 2 right parenthesis plus fraction numerator left parenthesis 2 right parenthesis thin space left parenthesis 2 minus 0 right parenthesis space left parenthesis 4 minus 0 right parenthesis over denominator 6 end fraction space equals space 6 plus 8 over 3 space equals space 26 over 3

87 Views

Advertisement
20.

Evaluate the following integrals as the limit of a sum
integral subscript 0 superscript 2 left parenthesis straight x squared plus 1 right parenthesis space dx

95 Views

Advertisement