Question

please answer this question​

Answer 1

The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.

What is integration?

It is the reverse of differentiation. The differentiation is the rate of change of the function with respect to variables.

The integration is given below.

$\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{(1 +x)^{2022}} \ dx$

Then the integration can be written as

$\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{[(1 +x)^{1011}]^2} \ dx$

Let (1 + x)¹⁰¹¹ = t. Then 1011x¹⁰¹⁰ dx = dt.

Then we have

$\rightarrow \int_{1}^{\infty } \dfrac{dt}{1011 \ t^2}$

Then integrate

$\rightarrow \dfrac{1}{1011} \left [ \dfrac{-1}{t} \right ]_{1}^{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ \dfrac{1}{t} \right ]^{1}_{\infty }\\\\\\\rightarrow \dfrac{1}{1011} \left [ 1- 0 \right ]\\\\\\\rightarrow \dfrac{1}{1011}$

The integration of the provided integration expression which is evaluated without using the beta function is equal to 1/1011.

More about the integration link is given below.

https://brainly.com/question/18651211

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