Find the integral using an appropriate trigonometric substitution. $\int \frac{x}{\sqrt{4-x^{2}}} d x$
A) $-\sqrt{4-x^{2}}+C$
B) $\sqrt{2-x}+C$
C) $\sqrt{4-x^{2}}+C$
D) $-\sqrt{2-x}+C$

Question

Quizplus · Accepted Answer

The integral can be solved using the substitution $x = 2\sin(\theta)$, which simplifies the integral to $\int \cos(\theta) d\theta$, resulting in $-\sqrt{4-x^{2}}+C$.

Find the Integral Using an Appropriate Trigonometric Substitution ∫x4−x2dx\int \frac{x}{\sqrt{4-x^{2}}} d x∫4−x2​x​dx

Find the Integral Using an Appropriate Trigonometric Substitution $\int \frac{x}{\sqrt{4-x^{2}}} d x$