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Which of the following is NOT true?

  • Option 1)

    \int_{a}^{b} f(x)dx = \int_{a}^{b}f(y)dy

  • Option 2)

    \int f(x)dx = \int f(t)dt

  • Option 3)

    \int_{a}^{b} f(x)dy = \int_{a}^{b}f(y)dx

  • Option 4)

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

 

Answers (1)

best_answer

As we have 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

 

 

 The variables are different is in both the integrals.

 


Option 1)

\int_{a}^{b} f(x)dx = \int_{a}^{b}f(y)dy

Option 2)

\int f(x)dx = \int f(t)dt

Option 3)

\int_{a}^{b} f(x)dy = \int_{a}^{b}f(y)dx

Option 4)

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

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