How do you integrate #int6dx/(sqrt(4-(x-1)^2)#?
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To integrate ( \int \frac{6dx}{\sqrt{4 - (x-1)^2}} ), use the substitution method. Let ( u = x - 1 ), then ( du = dx ). After substitution, the integral becomes ( \int \frac{6du}{\sqrt{4 - u^2}} ). This integral represents the arc sine function. So, the integral evaluates to ( 6\arcsin\left(\frac{u}{2}\right) + C ), where ( C ) is the constant of integration. Finally, substitute back ( u = x - 1 ) to get the final result: ( 6\arcsin\left(\frac{x - 1}{2}\right) + C ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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