`int_0^4 1/sqrt(x) dx` Explain why the integral is improper and determine whether it diverges or converges. Evaluate the integral if it converges The integral is improper because the function under the integral is not defined at zero (see the image below).

`1/sqrt0=1/0`

`int_0^4 1/sqrt x dx=2sqrt x|_0^4=2(sqrt 4-sqrt0)=4`

The integral converges and its value is equal to 4.

The image below shows graph of the function and area under it representing...

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The integral is improper because the function under the integral is not defined at zero (see the image below).

`1/sqrt0=1/0`

`int_0^4 1/sqrt x dx=2sqrt x|_0^4=2(sqrt 4-sqrt0)=4`

The integral converges and its value is equal to 4.

The image below shows graph of the function and area under it representing the value of the integral.

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