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Confused! kindly explain, - Integral Calculus - JEE Main-9

Which of the following is equal to integral  \int_{7}^{10}f(x)dx?

  • Option 1)

    \int_{10}^{7}f(x)dx

  • Option 2)

    \int_{7}^{10}f(t)dt

  • Option 3)

    \int_{-7}^{-10}f(x)dx

  • Option 4)

    none of these.

 
Answers (1)
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G gaurav

As we learnt,

 

Fundamental Properties of Definite integrals -

The value of the Definite integrals does not change with the change of variable of integration.

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

- wherein

a< x< b

a< t< b

 

 

 \int_{7}^{10}f(x)dx = \int_{7}^{10}f(t)dt

 


Option 1)

\int_{10}^{7}f(x)dx

Option 2)

\int_{7}^{10}f(t)dt

Option 3)

\int_{-7}^{-10}f(x)dx

Option 4)

none of these.

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