Consider the integral as attached, To determine the convergence or divergence of the integral, how many improper integrals must be analyzed? What must be true of each of these integrals for the given integral to converge? int_0^3 10/(x^2-2x)dx.

geduiwelh 2021-03-07 Answered
Consider the integral as attached, To determine the convergence or divergence of the integral, how many improper integrals must be analyzed? What must be true of each of these integrals for the given integral to converge?
0310x22xdx.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

l1koV
Answered 2021-03-08 Author has 100 answers

Step 1
Consider the integral 0310x22xdx.
To determine the convergence or divergence of the integral,and we need to analyze how many improper integrals are there.
and what must be true of each of these integrals for the given integral to converge.
Step 2
First we will see the dicontinuities of the function 10x22x
x22x=0x=0orx=2
We can write
0310x22xdx=lima0+ab10x22xdx+limc2bc10x22x+limd2d310x22x
Let c(0,2)
The integral must split in three improper integrals to contain one limit per integral. As 0 is the left integral limit we only need the right hand limit.
The dicontinuity at x=2 lies inside the interval (0,3) so we will consider both the limits.
Step 3
Now the limit must exists for all the three integrals to be convergent.
and each of the three integrals must be convergent for the integral 0310x22x dx to be convergent.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more