Let R be the region bounded by the curves x = 0, y = sin(x)+1, y = sin(x), and y = 2 − x. Find the area of R.
I need to use a transformation to find this, but I could not solve it using a transformation to a rectangle. How else, then could I evaluate it?
The R region is bounded by the red, green, and blue curves. Calculate first the intersections of y=2-x with the two sin curves, and you can write your integral as the sum of two parts.