- #1
Martyn Arthur
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- TL;DR Summary
- Area Integration
Hi I struggle with integration generally. Could you be able please to talk me through the stages of this one?
thanks
martyn
thanks
martyn
It would be helpful if you told us exactly which parts you don't understand. If your answer is "all parts," then my suggestion would be to go back to the start of the section in your textbook where iterated integration is introduced.Martyn Arthur said:Could you be able please to talk me through the stages of this one?
This integral is $$\int_{x=\pi/2}^\pi \sin(2y)~dy$$Martyn Arthur said:I am completely lost as to the overall mechanics of the conversion of sin to (-1/2cos).
Integral 2 is not the conclusion. It is the result of the integral in parentheses in integral 1.Martyn Arthur said:Given that integral 2 produces a conclusion how do they fit together.
I suspect at this level you are expected to recognise a common anti-derivative like this.Martyn Arthur said:I am completely lost as to the overall mechanics of the conversion of sin to (-1/2cos).
I can't make any sense of this of the attachments. They are the same image double-posted and are as follows:Martyn Arthur said:You guys are so patient. Given the following
xr^3(1-cos^2θ)cos^2θ
I need to make the substitution u = (1-cos^2θ) have I got it right?
Thanks
View attachment 340095
To integrate a function over a rectangular area, you first need to set up the double integral by defining the limits of integration for both the x and y variables. Then, you can evaluate the integral using the appropriate integration techniques.
Integrating a function over a rectangular area allows you to calculate the total value or quantity represented by the function within that specific region. This is useful in various fields such as physics, engineering, and economics to analyze and solve problems.
Sure! Let's say we have a function f(x, y) = x^2 + y defined over the rectangular area R: 0 ≤ x ≤ 2 and 0 ≤ y ≤ 3. To integrate this function over the area R, we would set up the double integral ∫∫R (x^2 + y) dA and evaluate it to find the total value within the region.
Yes, there are various techniques for integrating functions over a rectangular area, such as changing the order of integration, using polar coordinates, or applying symmetry properties to simplify the calculation. The choice of technique depends on the complexity of the function and the region.
Some common challenges when integrating functions over a rectangular area include setting up the correct limits of integration, dealing with discontinuities or singularities in the function, and ensuring the accuracy of the calculation by considering all possible scenarios within the region. Practice and familiarity with integration techniques can help overcome these challenges.