Finding area using double integral?

range of radius: r = [0,1]

range of angle: t = [0, pi]

here t stands for angle theta.

The area of a small element is dr * r dt. If you don't see why, draw an element whose coordinate (r, t) satisfying r0<r<r0+dr, t0<t<t0+dt, where r0 and t0 are two arbitrary number in the semi-circle. You can see that dr and r*dt are two sides of this element and so its area is dr * rdt.

You integral this small area to get the whole area:

int[t from 0 to pi] int [r from 0 to 1] r dr dt

= int[t from 0 to pi] 1/2 dt

= pi / 2

Hope this helps :)

Area Of A Circle Integral

gazing the graph of those 2 polar purposes, you opt to discover the section of the left 0.5 of the circle and subtract the section of the cardioid that is risk-free. The integrals will the two have an era of ?/2 to 3?/2 a million/2( ?(a million)^2*d? - ?(a million + cos?)^2*d? ) = a million.215