Question

1/√16-9ˣ²,Integrate the given function defined on proper domain w.r.t. x.

Answer 1

In the attachment I have answered this problem.          The solution is simple and easy to understand.         See the attachment for detailed solution.

Answer 2

Dear Student,

Answer: ∫ 1/√16-9x² dx$= \frac{1}{3} {sin}^{ - 1} ( \frac{3x}{4} ) + C$

Formula used:

∫ $\frac{1}{ \sqrt{ {a}^{2} - {x}^{2} } } dx = {sin}^{ - 1} ( \frac{x}{a} ) + C$

Take 9 common to convert given function in the above mentioned form

∫$\frac{1}{ \sqrt{16 - {x}^{2} } } dx \:$

∫$\frac{1}{3 \sqrt{ {( \frac{4}{3} })^{2} - {x}^{2} } } dx$

$= \frac{1}{3} {sin}^{ - 1} ( \frac{x}{ \frac{4}{3} } ) + C$

$= \frac{1}{3} {sin}^{ - 1} ( \frac{3x}{4} ) + C$

Hope it helps you.