please answer this question

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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.

[tex]\rightarrow \rm \int _0^{\infty} \dfrac{x^{1010}}{(1 +x)^{2022}} \ dx[/tex]

Then the integration can be written as

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

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

Then we have

[tex]\rightarrow \int_{1}^{\infty } \dfrac{dt}{1011 \ t^2}[/tex]

Then integrate

[tex]\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}[/tex]

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.

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Related Questions

Work out the size of angle x

Answers

take 180-123=57 u take 42+57=99

2.* Use the slope (m) and y-intercept (b)
to describe the system.
(1) x + y = -1
(2) -x - y=-1
F. Intersecting lines
G. Same lines, m > 0
H. Same lines, m < 0
J. Parallel lines, m > 0
K. Parallel lines, m < 0

Answers

Answer:

the answer is for this particular problem is F

Sam Bought a shirt for $27 after a discount, He said he bought the shirt at a 10% discount, What was the original selling price of the shirt?

Answers

Answer:$37.00

Step-by-step explanation: hope it helps

What is the radius of oT?
Answer Here
+
21
20
R

Answers

The length of the half chord is given as 21. The length of the perpendicular drawn from the center to the chord is 20. The radius would be 29 units.

What is Pythagoras' Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).

The length of the half chord is given as 21.

The length of the perpendicular drawn from the center to the chord is 20.

By Pythagoras' Theorem

[tex]|r|^2 = |21|^2 + |20|^2\\\\|r|^2 = 441 + 400\\\\|r|^2 = 841\\\\|r| = \sqrt{841} \\\\r = 29[/tex]

The radius of the circle would be 29 units.

Learn more about Pythagoras' theorem here:

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rewrite! Write an new and equivalent equation that is easier to solve

Answers

[tex]{\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}[/tex]

[tex] \sf 7( \sqrt{m + 1} - 3) = 21[/tex]

we will multiply 7 with bracket

[tex] \sf 7 \sqrt{m + 1} - 21 = 21[/tex]

Now we will take (-21) on LHS to RHS

[tex] \sf 7 \sqrt{m + 1} = 21 + 21 \\ \\ \sf7 \sqrt{m + 1 } = 42 \\ \\ \sf \sqrt{m + 1} = \frac{42}{7} \\ \\ \sf \sqrt{m + 1} = 6[/tex]

Now we will do squaring both sides

[tex] \sf {( \sqrt{m + 1}) }^{2} = {(6)}^{2} \\ \\ \sf \red {m + 1 = 36}[/tex]

[tex]\sf{ 7( \sqrt{m+1} - 3)=21}[/tex]