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  • Need clarity, kindly explain! - Integral Calculus - JEE Main-9

\int_{a}^{c}f(x)dx = \int_{a}^{b}f(x)dx + \int_{b}^{c}f(x)dx is not true if

  • Option 1)

    a\leqslant c \leqslant b

  • Option 2)

    a \leqslant b \leqslant c

  • Option 3)

    a = b =c

  • Option 4)

    Its always true.

 

Answers (1)

best_answer

As we learnt,

 

Fundamental Properties of Definite integration -

If the function is continuous in (a, b ) then integration of a function a to b will be same as the sum of integrals of the same function from a to c and c to b.

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

- wherein

 

 

 

This condition is always true no mater where x =c lies.

 


Option 1)

a\leqslant c \leqslant b

Option 2)

a \leqslant b \leqslant c

Option 3)

a = b =c

Option 4)

Its always true.

Posted by

gaurav

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