aiman altaf

aiman altaf

Answered question

2022-06-05

 

Answer & Explanation

karton

karton

Expert2023-05-19Added 613 answers

The integral 14dxx3 is improper because it exhibits one or more of the following characteristics:
1. **Infinite limits**: The denominator (x3) becomes zero at x=3, which results in a division by zero. This leads to an undefined value in the integrand, and as a result, the integral cannot be evaluated at x=3. Since the interval of integration includes x=3, the limits of integration are infinite.
2. **Discontinuity**: The integrand has a discontinuity at x=3 due to the division by zero. This introduces a jump or gap in the function, making it discontinuous over the interval of integration.
In this case, the integral is improper because it violates the fundamental conditions required for a proper integral, which include having finite limits and a continuous integrand over the interval of integration.

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