find the average value of the function
over the plane region R is the triangle with vertices (0,0), (1,0) and (1,1)
calculus - MathMate, Monday, April 2, 2012 at 10:10am
The triangle is bounded by
The integrals can be carried out in order dx, then dy or vice-versa.
However, integrating with respect to dy first makes for an easier integration (in the evaluation of I).
Be very sure you understand how the limits are obtained. Draw a sketch of the triangle, and follow the limits, and it will be easy to visualize how the limits can be found.
Area, A = ∫∫dxdy
Limits of integration
y from 0 to x
x from 0 to 1
Integral of values
within the same limits