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n05tr4d4177u5
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i have been told that dA=R dR d(theta), what does mean exactly in terms of pi. the shape is a semicircle. Does this mean that d(theta) is 180, or pi. Please give me an example.
You do know how to integrate, don't you?n05tr4d4177u5 said:here is an example of mine that i have
suppose i hae a rectangle,
in a rectangles case, dA = dX dY
if i have the rectangles width and it is 4 m, then dA = 4dY,
which let's me integrate along y axis,
now for a semicircle, how would i do that if dA = r dr d(theta)
n05tr4d4177u5 said:in a rectangles case, dA = dX dY
if i have the rectangles width and it is 4 m, then dA = 4dY,
You are good up to here.n05tr4d4177u5 said:here is an example of mine that i have
suppose i hae a rectangle,
in a rectangles case, dA = dX dY
if i have the rectangles width and it is 4 m, then dA = 4dY,
Can you complete the above integral?which let's me integrate along y axis,
now for a semicircle, how would i do that if dA = r dr d(theta)
imagine the top half of a circle. the origin lies along the bottom of the semicircle, and in the middle. y-axis up, and x-axis to the right and left. i think theta can only go from 0 to 180 degrees since it is a semi circle. Y = d(theta) R squared
R = radius, integrate from 0 to R
(And arildno did not say he had never seen that before, he was trying to get you to think about why you think that was true.)in a rectangles case, dA = dX dY
if i have the rectangles width and it is 4 m, then dA = 4dY
The Semicircle Problem is a mathematical problem that involves finding the area of a semicircle by using the formula dA = R*dR*d(theta), where dA is the differential of the area, R is the radius, and d(theta) is the differential of the angle.
The formula dA=R dR d(theta) is derived using the concept of integration in calculus. By dividing the semicircle into infinitesimally small sectors, we can calculate the area of each sector using the formula for the area of a triangle, which is 1/2*base*height. Then, by summing up the areas of all the sectors, we can find the total area of the semicircle.
R represents the radius of the semicircle. It is a constant value and does not change as we move along the circumference of the semicircle.
The angle d(theta) represents the change in the angle of the semicircle. As the angle increases, the area of the semicircle also increases. This is because a larger angle corresponds to a larger arc length, which results in a larger area.
Yes, the same concept and formula can be applied to other shapes, such as circles and sectors. However, the value of R and the limits of integration may change depending on the shape being calculated.