∫√(16 9x^2)dx ∫√((4)^2 (3x)^2)dx [∫√(a^2 x^2)=x√(a^2 x^2)2+a^22sin^ 1xa] 3x√(16 9x^2)2+162sin^ 1(3x)4+c 3x2√(16 9x^2)+8sin^ 13x4+c . ...

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Functions

∫√16-9x2dx.

Question

$\int \sqrt{16 - 9 x^{2}} d x$ .

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Solution

$\int \sqrt{16 - 9 x^{2}} d x$
$\int \sqrt{(4)^{2} - (3 x)^{2}} d x$
$[\int \sqrt{a^{2} - x^{2}} = \frac{x \sqrt{a^{2} - x^{2}}}{2} + \frac{a^{2}}{2} {sin}^{- 1} \frac{x}{a}]$
$\frac{3 x \sqrt{16 - 9 x^{2}}}{2} + \frac{16}{2} {sin}^{- 1} \frac{(3 x)}{4} + c$
$\frac{3 x}{2} \sqrt{16 - 9 x^{2}} + 8 {sin}^{- 1} \frac{3 x}{4} + c$ .

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