High polar coordinates used to calculate double integral, do not understand the meaning, please guide

High polar coordinates used to calculate double integral, do not understand the meaning, please guide

In the double integral, D σ is the area in the plane coordinate (in the X-Y coordinate, DX and Dy are perpendicular to each other, and DXDY is the differential area directly). Then it is expressed in polar coordinates as ρ D, ρ D θ. In fact, what we understand is how to calculate the differential area in polar coordinates
First of all, the formula of polar coordinates for calculating area in high school is s = 1 / 2 · L · r = 1 / 2 · R & # 178; · α = 1 / 2 · ρ & # 178; · θ,
In differentiation, D σ = ρ D, ρ D θ, which is the graph on the first floor. ρ D θ is the arc of differentiation (the two arcs are approximately the same), and D ρ is the height of the differential rectangle. This is probably the way to understand it. It's easier to understand the knowledge in the book

How to determine the value range of independent variable

According to the specific situation, we should generally see whether there are requirements for the dependent variable. The range of the dependent variable should be calculated according to the dependent variable. We should also see that the number under the even root of the function formula should not be less than zero. If it is an exponential function, the logarithmic function should meet their requirements for the independent variable

The value range of independent variable
At the beginning, a businessman sold a certain commodity with a purchase price of 8 yuan per piece at 10 yuan per piece, and he could sell 100 pieces per day. He wanted to increase the selling price to increase the profit. Through the experiment, it was found that every 1 yuan increase in the price of this commodity would reduce the daily sales by 10 pieces. 1. Write the functional relationship between the daily profit y (yuan) and the selling price x (yuan / piece);
There must be a process, especially how to calculate the value range

After the price increase, the profit per piece is X-8, and the daily sales volume is reduced by (X-8) * 10
So y = (100 - (X-8) * 10) * (X-8)
= -10(x-13)^2+250
The maximum value of Y is 250 when x = 13
x> At 13, y decreases with the increase of X

What is the value range of function independent variable

=Rand () * (max min) + min
Or take random integer directly with the following formula
=RANDBETWEEN(1,5)
1 and 5 points plus the minimum and maximum

Find the value range of independent variable x
1.y=x^2-x+5

X is not equal to 0 because any power of 0 has no meaning

How to determine the range of independent variables from the image in mathematics?
There is no formula for a graph
Or what do you think? method

For example, if the maximum value of X is 5 and the minimum value of X is - 3, then the value range of the independent variable is - 3

It is known that the value range of independent variable x in a function y = 1-3x is greater than or equal to - 1 and less than or equal to 2?
.

Conversion
x=(1-y)/3
Because the value of X is [- 1,1]
Return to
Y value [- 2,4]

If the solution of the linear equation 3x-6 = 0 is x = 2, then when the value of the linear function y = 3x-6 is 0, the value of the independent variable x is ()
What is in brackets?

When y = 0, 3x-6 = 0, X is 2

How to find the value range of independent variable in function

The independent variable is the domain of the function. 1. The artificial definition depends on whether there is any artificial range. For example, the arctana definition of the inverse trigonometric function a should be between - 90 and 90 degrees. 2. The natural definition must be f (x) = 1 / x, X! = 0. The domain of the logarithmic function must be greater than 0 = = in short, if the formula is true, 3

Why does the value range of double integral r in polar coordinates sometimes multiply sin θ or cos θ by the upper limit and sometimes bring in the value?
For example, the upper limit of R is sometimes 2acos θ, sometimes 2

This is determined according to the integral region. If the integral region is a circle with the center of the circle at the origin and radius = 2, that is, x ^ 2 + y ^ 2 = 4, but if the center of the circle is not at the origin, for example, x ^ 2 + y ^ 2 = 2aX, according to the coordinate transformation of polar coordinates, x = RCOs θ is substituted into the circular equation
R ^ 2 = 2arcos θ, so the upper integral limit of R is 2acos θ