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  • Need explanation for: 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}^{2\pi}\sin xdx

  • Option 2)

    \int_{0}^{2\pi}\cos xdx

  • Option 3)

    \int_{0}^{2\pi}\tan xdx

  • Option 4)

    \int_{0}^{2\pi}e^{x}dx

 

Answers (1)

best_answer

As we have 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 f(x) = tanx is discontinous at x = \frac{\pi}{2},\frac{3\pi}{2}.

 


Option 1)

\int_{0}^{2\pi}\sin xdx

Option 2)

\int_{0}^{2\pi}\cos xdx

Option 3)

\int_{0}^{2\pi}\tan xdx

Option 4)

\int_{0}^{2\pi}e^{x}dx

Posted by

gaurav

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