Figure area enclosed by curve and straight line The area enclosed by the curve y = x ^ 3 + 1, the straight line x + y = 3 and two coordinates

It is suggested to use the knowledge of integration and the combination of number and shape to solve the problem. Drawing can show that they have intersection points in the first quadrant, and the intersection points (1,2) are obtained by solving the two equations simultaneously. The intersection points of the straight line and X axis are the area enclosed by (3,0) and calculated by two parts. (1). X = 0 to x = 1 are the areas under the curve by integration

Find the area of the figure enclosed by the curve
Find the area of the figure enclosed by the curves y = 1 / x, y = x and x = 2

By integral, the intersection of y = 1 / X and y = x (1,1) s = integral 1 - > 2 (x-1 / x) DX = 3 / 2-ln2

Find the area of the figure enclosed by the following curves
Y = 1 / 2x ^ 2, x ^ 2 + y ^ 2 = 8 (both parts need to be calculated)
The answer is 2pai + 4 / 3, 6pai-4 / 3

First calculate the intersection of the two images, and then use the integral to calculate the area. These two equations work out the intersection (2,2) and (- 2,2) as shown in the figure. First calculate the area of the above figure (that is, the black and red area). Because it is a symmetrical figure, only the red area is needed. The integral should be from 0 to 2

Find the area of the figure enclosed by ρ = cos α and ρ = 1-cos α
I don't understand how the figure of ρ = cos α is a circle and how the figure of ρ = 1-cos α is a heart. I really can't understand it. I've been thinking about it for a long time

This is a polar equation
Turn into ordinary equation
There are
ρ=cosα
→ρ²=ρcosα
→x²+y²=x
→（x-1/2）²+y²=1/4
So it's a circle

Kneeling to find the area of the figure enclosed by r = 1 and R = 2cosx

The first one is a circle, and the second one is whether you write theta as X, otherwise it is not polar coordinates. If it is polar coordinates, it is to shift the center of the first circle one unit to the right, so that the enclosed area is 2 × (π / 6-1 / 4 ×√ 3)

Find the area of the common part enclosed by the curves r = 2cos θ and R = 1
Is this problem not rigorous?

x^2+y^2=2x, x>=0
(x-1)^2+y^2=1 (1)
r=1,r^2=1
x^2+y^2=1 (2)
(2)-(1)
2x=1
x=1/2

Calculate the area of the figure enclosed by the following curves and lines
y=x2,y=x
Would you please write down the detailed process?

First, we calculate the two intersections ((0,0) and (1,1)), and then according to the graph, we find that the enclosed area is the area under the straight line minus the area under the curve
Area under 1 * 1 / 2 = 1 / 2 straight line
(x is between 0 and 1) ∫ x ^ 2 DX = [x ^ 3 / 3] = 1 / 3 this is the area under the curve
The enclosed area is 1 / 2 - 1 / 3 = 1 / 6

Find the area of the figure enclosed by the following curves and lines
y=2x^2 y=4
Here's the formula,

Points:
2 ∫ (4-2x ^ 2) DX (x from 0 to √ 2)#=
2(4x - 2/3x^3)
= 2(4√2 -4√2/3）
=2（8√2/3）
= （16/3）√2
#Originally it was from - √ 2 to √ 2 (y = 0 is the middle dividing line), but in this way, there can be less calculation, and it is more difficult to make mistakes

Find the area r = 2acost?
In a hurry

Polar equation: r = 2acost
The curve of polar coordinate equation is a circle whose center is in the radius of (a, 0)
Figure area & nbsp; = & nbsp; a & amp; sup2; π
See Fig
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Necing on the first floor, you also have a time when you are in a daze

If the line L is tangent to the circle x2 + y2 = 1 and the sum of the intercepts on the two axes is equal to 3, then the area of the triangle bounded by the line L and the two axes is equal to ()
A. 32B. 12C. 1 or 3D. 12 or 32

Let a line intersect X-axis at a (a, 0), Y-axis B (0, b), then | a | 1, | B | 1. The sum of intercept is equal to 3. The slope of line L is greater than 0. Let | ab | 0. Let | ab | = C, then C2 = A2 + B2 ① ∵ the line L is tangent to the circle x2 + y2 = 1, and the distance from the center of the circle (0,0) to the line AB is d = r = 1

Figure area enclosed by curve and straight line The area enclosed by the curve y = x ^ 3 + 1, the straight line x + y = 3 and two coordinates