Question

Evaluate the following:

`int ("d"x)/sqrt(16 - 9x^2)`

Answer 1

Let I = `int ("d"x)/sqrt(16 - 9x^2)`

= `1/3 int ("d"x)/sqrt(16/9 - x^2)`

= `1/3 int ("d"x)/sqrt((4/3)^2 - x^2)`

= `1/3 sin^-1  x/(4/3) + "C"`  ....`[because int ("d"x)/sqrt("a"^2 - x^2) = sin^-1  x/"a" + "C"]`

∴ I = `1/3 sin^-1  (3x)/4 + "C"`