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Step-by-step Solution

Integral of (9-4x^2)^0.5

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Answer

$\frac{9}{4}arcsin\left(\frac{2}{3}x\right)+\frac{1}{2}\sqrt{9-4x^2}x+C_0$

Step-by-step explanation

Problem to solve:

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

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

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

Taking the constant out of the radical

$\int2\sqrt{\frac{9}{4}-x^2}dx$

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Answer

$\frac{9}{4}arcsin\left(\frac{2}{3}x\right)+\frac{1}{2}\sqrt{9-4x^2}x+C_0$

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