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\int\left(\sqrt{9-4x^2}\right)dx

Integrate (9-4x^2)^0.5

Answer

$\frac{9}{4}\left(\frac{2\sqrt{9-4x^2}x}{9}+arcsin\left(\frac{2}{3}x\right)\right)+C_0$

Step-by-step explanation

Problem

$\int\left(\sqrt{9-4x^2}\right)dx$
1

First, factor the terms inside the radical for an easier handling

$\int\sqrt{4\left(\frac{9}{4}-x^2\right)}dx$

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Answer

$\frac{9}{4}\left(\frac{2\sqrt{9-4x^2}x}{9}+arcsin\left(\frac{2}{3}x\right)\right)+C_0$

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