How to calculate the area of irregular figure

How to calculate the area of irregular figure

By cutting and complementing method, one or several regular figures can be calculated after translation and rotation, or the number of each part can be calculated by cutting method, and then added up

How to calculate the area of irregular figure?

For the area of irregular graphics, they are usually divided into several triangles. Calculating the area of triangles is relatively simple. S = absic, but how to divide, you need to divide according to the conditions of the topic to the situation that the edges and corners are known or easy to find

It's a little difficult to calculate the area of irregular figures
How to measure the area of an irregular fish candy?
Who's smarter

You can try this method. If the depth of the fish pond is the same everywhere, you can use the method of irrigation to fill the fish pond, record the volume of the water, and then just look at the water meter. Then, measure the depth of the water, and divide the volume by the depth to get the area of the fish pond

How to determine the upper and lower limits of integration when calculating arc length by polar coordinate equation?

According to the start and end of the arc to determine ah

On the definition of polar coordinate equation
Definition of polar coordinate equation: [in general, in polar coordinate system, if at least one of the polar coordinates of any point on the plane curve C satisfies the equation f (ρ, θ) = 0, and the coordinates suitable for the equation f (ρ, θ) = 0 are all on the curve C, then the equation f (ρ, θ) = 0 is called the polar coordinate equation of curve C.]
So how to understand "at least one satisfies the equation"?

Note that the polar representation of the point is not unique
For example, (ρ = 1, θ = 0) and (ρ = 1, θ = 2 π) represent the same point (x = 1, y = 0)
A point on a curve needs only one of the equations that satisfies the curve

How to use trapezoidal method to calculate definite integral

It is to divide the required parts into small trapezoids (similar to small rectangles, but in the case of the same number of divisions, it should be more accurate than the rectangular method)

Trapezoidal method 4. Write the program of using trapezoidal method to calculate definite integral. The integrand function can be sin (x) + ex, the integral interval [1,3]

#include
#include
using std::cout;
using std::endl;
double fun(double x){
return sin(x)+exp(x);
}
int main(){
double result=0;
double x=0;
double h=1e-6;
while(x

How to calculate the area enclosed by parabola and horizontal axis with definite integral

For example, if f (x) = PX ^ 2, after integration = 1 / 3px ^ 3, it can be solved by Newton Leibniz formula

For the definite integral ∫ root sign 1 + cos2xdx, the upper limit of the integral is π, and the lower limit of the integral is 0?

∵cos2x=2cos²x-1
∴∫√(1+cos2x)dx=∫√2|cosx|dx
∴(0,π)∫√(1+cos2x)dx=(0,π/2)∫√2cosxdx+(π/2,π)∫-√2cosxdx=2√2

For definite integral, the upper limit is 2, the lower limit is 0, and the answer to (1 + cosx) de under the root sign is 4, and the root sign is 2

√（1+cosx)
=√[1+2cos^2(x/2)-1]
=√[2cos^2(x/2)]
=√2*cos(x/2)
∫[0,π/2]√（1+cosx)dx
=∫[0,π/2]√2*cos(x/2)dx
=2√2sin(x/2)[0,π/2]
=2√2*√2/2
=2