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  • Confused! kindly explain, - Integral Calculus - JEE Main-10

What is the value of integral \int_{-a}^{a}f(x)dx equal to ?

  • Option 1)

    - \int_{a}^{a}f(x)dx

  • Option 2)

    -\int_{-a}^{a}f(x)dx

  • Option 3)

    \int_{a}^{-a}f(-x)dx

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learnt,

 

Fundamental Properties of Definite integration -

Interchanging the limit of the definite integral does not change the absolute value but change the sign of the integral.

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

- wherein

         

 

 

 \int_{-a}^{a}f(x)dx = \int_{a}^{-a}f(-x)dx

Since,

\int_{a}^{-a}f(-x)dx = \int_{-a}^{a}f(x)dx

 


Option 1)

- \int_{a}^{a}f(x)dx

Option 2)

-\int_{-a}^{a}f(x)dx

Option 3)

\int_{a}^{-a}f(-x)dx

Option 4)

none of these

Posted by

gaurav

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