Thank you in advance,I was just wondering if anybody knows why the

[jherd]

Thank you in advance,

I was just wondering if anybody knows why the integral of a 1/2 with respect to theta = pi?

Thanks

 

[stevenb]

Thank you in advance,

I was just wondering if anybody knows why the integral of a 1/2 with respect to theta = pi?

Thanks

What are the limits of integration?

If the limits are 0 to 2pi, then the answer is simple

[tex]\int_0^{2\pi}0.5 d\theta=0.5[\theta]_0^{2\pi}=0.5(2\pi)=\pi [/tex]

 

[micromass]

These question can also be easily answered by www.wolframalpha.com/
It can even show steps in solving the integral!

 

[jherd]

Thank you! Makes sense!

 

[CellCoree]

for your question. The integral of 1/2 with respect to theta is equal to pi because the integral of a constant is equal to that constant multiplied by the variable of integration. In this case, the variable of integration is theta, so we can rewrite the integral as 1/2 times theta. When we integrate from 0 to pi, we are essentially finding the area under the curve of 1/2 times theta, which is a triangle with base pi and height 1/2. Therefore, the area is equal to 1/2 times pi, or pi/2. I hope this explanation helps!