Question
Use integration by parts to obtain the formula$$\int \sqrt{1-x^{2}} d x=\frac{1}{2} x \sqrt{1-x^{2}}+\frac{1}{2} \int \frac{1}{\sqrt{1-x^{2}}} d x$$
Step 1
We can rewrite this integral in terms of trigonometric functions by using the substitution $x = \sin(t)$, which implies $dx = \cos(t) dt$. The integral then becomes $\int \sqrt{1-\sin^{2}(t)} \cos(t) dt = \int \cos^{2}(t) dt$. Show more…
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