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Anonymous users2024-02-06The integration region is divided into two pieces by the straight line x+y= 2
d1：0≤y≤π/4，y≤x≤π/2-y
d2: 4 x 2, 2-x y x therefore the original formula = (0, 4)dy (y, 2-y) cos(x+y) dx
/4，π/2)dx∫(π/2-x，x) cos(x+y) dy∫(0，π/4) (1-cos2y) dy∫(π/4，π/2) (cos2x-1) dx∫(0，π/2) (1-cos2x) dxx - 1/2*sin2x |0, 2) Meaning. When the integrand is greater than zero, the double integral.
is the volume of the cylinder.
When the integrand is less than zero, the double integral is the negative value of the cylinder volume.
in a spatial Cartesian coordinate system.
, the double integral is the algebraic sum of the volume of the cylinder over each part region, the positive above the xoy plane and the negative below the xoy plane. Some special formulas for the volume of the top cylinder of the curved top surrounded by the surface represented by the integrand f(x,y) and the bottom surface of d.
It is known that it can be calculated in terms of the geometric meaning of the double integral.
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Anonymous users2024-02-05The following process is for the subject's reference.
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Anonymous users2024-02-04This solution is the area of the region d, d is a ring, the outer radius is 2, the inner radius is 1, so the area of the ring is 4 3
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Anonymous users2024-02-03According to the definition of the double integral, the integral function f(x,y)=1 of the double integral d is obtained, the integral region d is a ring surrounded by a radius of r1=2 and a radius of r1=1, and the double integral is essentially the area of the circle of the integral region, that is, d = r1 - r2 = (2 -1)=3, and the solution process is shown in the following figure
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Anonymous users2024-02-02According to the number protection.
The answer is clnx, which is less than 0 at x (1).
So the integral is less than 0
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Anonymous users2024-02-01In the area of the integrand, the integrand is less than 0, so the integral is negative.
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Anonymous users2024-01-31The answer C method is shown in the figure below, please check it carefully, and I wish you a happy study:
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Anonymous users2024-01-30The method is shown in the figure below, please check it carefully, and I wish you a happy study:
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Anonymous users2024-01-29Points (x,y) within the integration region d
x＋y∈[0，1]
x＋y≥(x＋y)²
x y)dxdy x y) dxdy: select ay= x and y=x 1 as ( 1 2, 1 2) d (x y)dxdy
－1/2，0) dx∫(－x，x＋1) (x＋y)dy∫(－1/2，0) (2x²＋2x＋1/2)dx(2/3 x³＋x²＋1/2 x)|(1/2，0)∫d (x＋y)²dxdy
－1/2，0)dx∫(－x，x＋1) (x²＋2xy＋y²)dy∫(－1/2，0) (8/3 x³＋4x²＋2x＋1/3)dx(2/3 x^4＋4/3 x³＋x²＋1/3 x)|(1/2，0)
Since you said that it is the first semester of your junior year, then I advise you to focus more on professional courses, because professional courses also have to be studied well, and it is not too late to prepare for the next semester!!
I'd like to ask what the t in the first question is ...... >>>More
An infinitesimal is a number that is infinitely close to zero, but not zero, for example, n->+, (1, 10) n=zero)1 This is an infinitesimal and you say it is not equal to zero, right, but infinitely close to zero, take any of the values cannot be closer to 0 than it (this is also the definition of the limit in the academic world, than all numbers ( ) are closer to a certain value, then the limit is considered to be this value) The limit of the function is when the function approaches a certain value (such as x0) (at x0). 'Nearby'The value of the function also approaches the so-called existence of an e in the definition of a value, which is taken as x0'Nearby'This geographical location understands the definition of the limit, and it is no problem to understand the infinitesimite, in fact, it is infinitely close to 0, and the infinitesimal plus a number, for example, a is equivalent to a number that is infinitely close to a, but not a, how to understand it, you see, when the chestnut n->+, a+(1, 10) n=a+ is infinitely close to a, so the infinitesimal addition, subtraction, and subtraction are completely fine, and the final problem of learning ideas, higher mathematics, is actually calculus, and the first chapter talks about the limit In fact, it is to pave the way for the back, and the back is the main content, if you don't understand the limit, there is no way to understand the back content, including the unary function, the differential, the integral, the multivariate function, the differential, the integral, the differential, the equation, the series, etc., these seven things, learn the calculus, and get started.
So far, I think that all knowledge always has its interconnected parts. >>>More
Knowledge points to memorize, I personally feel that the knowledge points before college are few and easy to remember, anyway, I almost never memorized mathematical formulas or theorems in junior high and high school, and if I can't remember, I will take the exam, but there is too much mathematical content in college, and derivation is also very troublesome, so I have to remember those formulas. Then you have to brush the questions, more brushing questions helps to understand the use of knowledge, you can see some of the famous teachers, I feel that what the teacher said will help to understand some, if you can find someone to communicate with you about the problem, it is the best.