Answer:
The sum of the area of the shaded regions = 0.248685
Explanation:
The sum of the area of the shaded region is given as follows;
The point of intersection of the graphs are;
y = x/2
y = sin²x
∴ At the intersection, x/2 = sin²x
sinx = √(x/2)
Using Microsoft Excel, or Wolfram Alpha, we have that the possible solutions to the above equation are;
x = 0, x ≈ 0.55 or x ≈ 1.85
The area under the line y = x/2, between the points x = 0 and x ≈ 0.55, A₁, is given as follows
1/2 × (0.55)×0.55/2 ≈ 0.075625
The area under the line y = sin²x, between the points x = 0 and x ≈ 0.55, A₂, is given using as follows;
Therefore;
![A_2 = \int\limits^{0.55}_0 {sin^2x} \, dx = \dfrac{1}{2} \left [x -sin(x) \cdot cos(x) \right]_0 ^{0.55}](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cint%5Climits%5E%7B0.55%7D_0%20%7Bsin%5E2x%7D%20%5C%2C%20dx%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Cleft%20%5Bx%20-sin%28x%29%20%5Ccdot%20cos%28x%29%20%5Cright%5D_0%20%5E%7B0.55%7D)
∴ A₂ =1/2 × ((0.55 - sin(0.55)×cos(0.55)) - (0 - sin(0)×cos(0)) ≈ 0.0522
The shaded area, 
= A₁ - A₂ = 0.075625 - 0.0522 ≈ 0.023425
Similarly, we have, between points 0.55 and 1.85
A₃ = 1/2 × (1.85 - 0.55) × 1/2 × (1.85 - 0.55) + (1.85 - 0.55) × 0.55/2 = 0.78
For y = sin²x, we have;
![A_4 = \int\limits^{1.85}_{0.55} {sin^2x} \, dx = \dfrac{1}{2} \left [x -sin(x) \cdot cos(x) \right]_{0.55} ^{1.85} \approx 1.00526](https://tex.z-dn.net/?f=A_4%20%3D%20%5Cint%5Climits%5E%7B1.85%7D_%7B0.55%7D%20%7Bsin%5E2x%7D%20%5C%2C%20dx%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Cleft%20%5Bx%20-sin%28x%29%20%5Ccdot%20cos%28x%29%20%5Cright%5D_%7B0.55%7D%20%5E%7B1.85%7D%20%5Capprox%201.00526)
The shaded area, 
= A₄ - A₃ = 1.00526 - 0.78 ≈ 0.22526
The sum of the area of the shaded regions, ∑A = +
∴ A = 0.023425 + 0.22526 = 0.248685
The sum of the area of the shaded regions, ∑A = 0.248685
Answer: what the heck of questions is this
Explanation:
The Cold War was fought after WWII from 1945 - 1991 between the US and democratic nations and the USSR and the Communist nations. They fought many 'proxy wars' such as, for example, but not limited to:
- Korean War
- Cuban missile crisis
The Cold War was named the way it is, because the two sides didn't fight head on head (as stated above). Instead, they supplied groups they are allied with, with volunteers, weapons & technology, as well as economic boosts. The Cold War saw the advancement of technology in many regions, including missiles, space technology, and other military technology.
Towards the end of the Cold War, the USSR had internal troubles, including satellite nations that wanted more freedom and democracy, as well as problems with the economy. Soon, the then-USSR leader, Mikhail Gorbachev, allowed <em>Glasnot</em>, or opennes, which ended the USSR's rule in 1991. He led the domestic reform and nuclear disarmament to help end the cold war, but because of internal factors, helped brake apart the USSR and lead to the downfall of communism in Europe.
However, Communism still continued in other nations, such as Cuba, Vietnam, & North Korea, but soon gave way to either a totalitarian state, or glasnot as well, as they either accepted US intervention and trade agreements (such as Vietnam) , or closed off even more (such as North Korea).
Even though people living during the Cold War had to live in fear, the Cold War helped bring the world more together, to give the world was able to draw closer together. The Cold War also spurred technological development (however mostly in the military), and helped create many organizations that helped countries around the world (such as the Peace Corps) and to further explore the world we live in as well as the surroundings (NASA). It also saw the creation of military alliances (NATO) as well as trading organizations, such as the World Trade Organization (WTO) and the North American Free Trade Organization (NATO) (in which the WTO is the whole world, while NATO was only Canada, USA, and Mexico).
hope this helps
Dx/dt=3
y=3x^3-2x
dy/dt=(9x^2)(dx/dt)-2(dx/dt)
When x= -2
dy/dt=(9(-2)^2)(3)-2(3)
=36(3)-6
=102
