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  • Please,please help me Which of the following integrals dont satisfy the condition for integration?

Which of the following integrals dont satisfy the condition for integration?

  • Option 1)

    \int_{0}^{5} x^{2}dx

  • Option 2)

    \int_{0}^{1} \left\{x \right \}dx

  • Option 3)

    \int_{0}^{3} [x]dx

  • Option 4)

    \int_{0}^{2} xdx

 

Answers (1)

best_answer

As we learnt,

 

Condition for definite integration -

f\left ( x \right ) must be continuous between a and b.
 

- wherein

\int_{a}^{b}f\left ( x \right )dx=

\left ( F\left ( b \right )+c \right )-\left ( F\left ( a \right )+c \right )

\Rightarrow F\left ( b \right )+X-F\left ( a \right )-X

\therefore F\left ( b \right )-F\left ( a \right )

 

 Since the function [x] is discontinous ar x = 1,2

 


Option 1)

\int_{0}^{5} x^{2}dx

Option 2)

\int_{0}^{1} \left\{x \right \}dx

Option 3)

\int_{0}^{3} [x]dx

Option 4)

\int_{0}^{2} xdx

Posted by

prateek

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