/sci/ - Science & Math

How do I geometrically express integration on the unit circle from 0 to PI/2
in terms of the area under the curve for [math]\int_{0}^{\pi/2}e^{ix}dx[/math] ? Should the yellow area be equal the sum of the blue and green? It is not.
Both integrals for sin and cos = 1, so the result is 1+i which has the magnitude of sqrt(2). But the area of 1/4 of the unit circle is PI/4. What gives?

How do I geometrically express integration on the unit circle from 0 to PI/2
in terms of the area under the curve for [math]\int_{0}^{\pi/2}e^{ix}dx[/math]?
Should the yellow area be equal the sum of the blue and green? It is not.
Both integrals for sin and cos = 1, so the result is 1+i which has the magnitude of sqrt(2). But the area of 1/4 of the unit circle is PI/4. What gives?