Integrating Sin(x): Solve the Area of a Half Circle

Karim Habashy · Mar 5, 2016

Hi All,

This is a very elementary question but, from calculus :

∫sinx dx from 0 to pi = 2, but i thought of it, in terms of the attached driagram.

And if we think of it, this way, the integration is the area of a half circle of radius one and is equal to Pi/2.

Where did i go wrong ?

blue_leaf77 · Mar 5, 2016

Karim Habashy said:

And if we think of it, this way, the integration is the area of a half circle of radius one and is equal to Pi/2.

No, it's not. Your mistake was to assume ##x## as the coordinate in the horizontal line, when it's actually the angle subtended between the line and the horizontal axis.

Karim Habashy · Mar 5, 2016

You are right, thanks. the integration would be ∫(sinx)²dx which is Pi/2.

Integrating Sin(x): Solve the Area of a Half Circle

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