Alternative text: Douglas Rennehan – Science!
Alternative text: I=\int\limits_a^b \frac{dx}{\sqrt{((b-x)(x-a))}}
Alternative text: u=\sqrt{b-x},
Alternative text: du=-\frac{1}{2}\frac{dx}{\sqrt{b-x}}
Alternative text: I=-2\int\limits_{u_1}^{u_2} \frac{du}{\sqrt{x-a}}
Alternative text: u_2
Alternative text: u_1
Alternative text: x
Alternative text: u_2
Alternative text: u_1
Alternative text: u^2=b-x
Alternative text: x=b-u^2
Alternative text: x-a=b-u^2-a
Alternative text: \sqrt{x-a}=\sqrt{b-a-u^2}
Alternative text: I=2\int\limits_{u_2}^{u_1} \frac{du}{\sqrt{(b-a)-u^2}}
Alternative text: I= \frac{2}{\sqrt{b-a}}\int\limits_{u_2}^{u_1} \frac{du}{\sqrt{1-(\frac{u}{\sqrt{b-a}})^2}}
Alternative text: y=\frac{u}{\sqrt{b-a}}
Alternative text: dy=\frac{du}{\sqrt{b-a}}
Alternative text: I=\frac{2}{\sqrt{b-a}}\int\limits_{y_1}^{y_2} \frac{\sqrt{b-a}}{\sqrt{1-y^2}} dy
Alternative text: I=2\int\limits_{y_1}^{y_2} \frac{1}{\sqrt{1-y^2}} dy
Alternative text: arcsin(y)
Alternative text: y=\sin{\theta},
Alternative text: dy=\cos(\theta)d\theta
Alternative text: I=2\int\limits_{\theta_1}^{\theta_2} \frac{\cos(\theta)}{\sqrt{1-\sin^2{\theta}}} d\theta
Alternative text: I=2\int\limits_{\theta_1}^{\theta_2} d\theta
Alternative text: 1-\sin^2{\theta}=\cos^2{\theta}
Alternative text: \theta_2
Alternative text: \theta_1
Alternative text: I=2(\theta_2-\theta_1)
Alternative text: \theta_2
Alternative text: \theta_1
Alternative text: u_i
Alternative text: u_2=\sqrt{b-b}=0
Alternative text: u_1=\sqrt{b-a}
Alternative text: y_i
Alternative text: y_2 =\frac{\sqrt{b-a}}{\sqrt{b-a}}=1
Alternative text: y_1=\frac{0}{\sqrt{b-a}}=0
Alternative text: \theta_2 = \arcsin{1} = \frac{\pi}{2}
Alternative text: \theta_1=\arcsin{0}=0
Alternative text: I=2(\frac{\pi}{2}-0)
Alternative text: I=\pi
Alternative text: a,b\in\mathbb{R}
Alternative text: I
Alternative text: \pi
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