Question

Determine whether the improper integral converges or diverges, and find the value if it converges.

[infinity]
∫ 3/2x^2. dx
5

Answer 1

Integral will be diverging in nature

Explanation:

We have given integral
`\int_(5)^(\infty)(3)/(2)x^2dx`

Now after solving the integral

`[(3)/(2)(x^3)/(3)]` limit from 5 to infinite

So
`[(3)/(2)(\infty^3)/(3)]-[(3)/(2)* (5^3)/(3)]=\infty`

As after solving integral we got infinite value so integral will be diverging in nature