Question

Using integration find the area of the region {(x,y):9x^2+y^2=36 and 3x+y=6}

Answer 1

Answer:

Step-by-Well, this is the area above the line and below an ellipse with a=2,b=6. The area of an ellipse is πab, so the area of this ellipse is 12π. We are only interested in the top right quadrant, and the area of this is 3π.

From this we want to subtract the area below the line 6−3x, which is given by

∫206−3xdx=6x−3x22∣∣∣20=6

so the area is given by

A=3π−6step explanation: