U=\frac{a\pih^2a}{m} \int\limits^a_b {x} \, dx \pi d^3 x l w (x) l^4 evaluate it

Mathematics

1 answer:

blsea [12.9K]3 years ago

8 0

I'm interested in integrals of the form

I(a,b)=∫

∞

arccot(x)⋅arccot(ax)⋅arccot(bx) dx, for a>0,b>0

It's known†Gradshteyn & Ryzhik, Table of Integrals, Series, and Products, 7th edition, page 599, (4.511) that

I(a,0)=

π2

[ln(1+

ln(1+a)

Maple and Mathematica are also able to evaluate

I(1,1)=

3π2

ln2−

ζ(3).

You might be interested in

six friends are going to buy a pizza. Their chices are to biu 2 medium 10-inch diameter pizzas for 7:00 each, or 1 large 14 inch

11111nata11111 [884]

For this question, we want to find out the greatest amount of area of pizza for the least amount of money:

So we have two pizzas with a 10 in. diameter. Let us take one of those pizzas.

The formula for area of a circle is $\pi r ^2$ ; So the area for one of these 10 in. pizzas would be $\pi (5)^2$ or 25 $\pi$ .

We have two of these pizzas, so the total area that we would get with $14 would be 25 $\pi$ *2 or 50 $\pi$ .

For the second case, we have one pizza with a 14 in. diameter.

The area of this pizza will be $\pi (7)^2$ or 49 $\pi$ .

So for $15 we can buy 49 $\pi$ worth of pizza.

The best deal would be to buy the two medium pizzas of 10 inch diameter, because for $14, you get 50 $\pi$ .

5 0

3 years ago

Which expressions are equivalent to ln x 2 ln 5 ln 1? Check all that apply. 2 ln 5x ln (x 26) ln 25x ln 1 ln 25x.

Marysya12 [62]

Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same.The expressions which are equivalent to the given expression are,

$\ln25+\ln1$
$\ln25$

Given information-

The expression given in the problem is,

$\ln x+2 \ln 5 +\ln1$

<h3>Equivalent expression-</h3>

Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same.

For given expression,

$\ln x+2 \ln 5 +\ln1$

As the above function is the function of <em>x. </em>Thus it can be written as,

$f(x)=\ln x+2 \ln 5 +\ln1$