Calculate the indefinite integral
$\int \frac{4 d x}{\sqrt{36 - 9 x^{2}}}$

Answer

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Answer

$\frac{4}{3} \sin^{- 1} (\frac{x}{2}) + C$ is the final answer.

Steps

Step 1 ：We are given the integral $\int \frac{4 d x}{\sqrt{36 - 9 x^{2}}}$ .

Step 2 ：This integral is in the form of $\int \frac{a d x}{\sqrt{b^{2} - a^{2} x^{2}}}$ , which is equal to $\frac{1}{a} \sin^{- 1} (\frac{a x}{b}) + C$ .

Step 3 ：In our case, a = 3, b = 6 and the constant multiplier is 4.

Step 4 ：We substitute these values into the formula to get the result.

Step 5 ：The result is given in piecewise form, which means the result is different depending on the value of x. However, since we're dealing with real numbers, we can ignore the part with the imaginary unit 'I'.

Step 6 ：The final result is $\frac{4}{3} \sin^{- 1} (\frac{x}{2}) + C$ .

Step 7 ： $\frac{4}{3} \sin^{- 1} (\frac{x}{2}) + C$ is the final answer.

Calculate the indefinite integral∫4dx36−9x2

Answer

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Calculate the indefinite integral
$\int \frac{4 d x}{\sqrt{36 - 9 x^{2}}}$