Polar Coordinates Evaluate double integral(R) (1/x) dA, where R is the region in
ID: 3545658 • Letter: P
Question
Polar Coordinates
Evaluate double integral(R) (1/x) dA, where R is the region in the first quadrant that lies inside the circle r = 3cos(theta) and outside the cardioid r = 1 + cos(theta).
Use polar coordinates to evaluate double integral(R) (ln(x^2 + y^2 + 2))dA, where R is the region inside the circle x^2 +y^2 = 4 in the first quadrant.
Not Polar Coordinates
Evaluate the given inetgral by reversing the order of integration (outer integral(0,1) inner integral(sin^-1(y),pi/2) cos x sq rt(1 +cos^2(x)) dxdy.
Sketch the type one and type two region of integration and show that (outer integral(0,4) inner integral(sqrt(y),2) sqrt(x^3+1)) dxdy = 52/9
Explanation / Answer
1.Now since both curves are symmetrical about the x-axis, we only need to calculate area above x-axis and double it.
Check out second image in link. We need to calculate area of blue region (and then double it).
Area of blue and pink regions = area of cardioid on interval [?/3, ?]
Area of pink region = area of circle on interval [?/3, ?/2]
Area of blue region = area of blue&pink regions - area of pink region
Area of blue region
= area of cardioid on interval [?/3, ?] - area of circle on interval [?/3, ?/2]
=