Question

resolva a integral ∫ dx/raiz 49-x2 obs: faca x=7sen(x)

Answer 1

Substituiçao trigonometrica:

x = 7sen(u)

dx = 7cos(u)du

Raiz(49-x²) = 7cos(u)

Fazendo a substituiçao na integral:

$\int\limits^{}_{}  \frac{7cos(u)du}{7cos(u)} du \\\\\int\limits^{}_{}  \frac{du}{1} du\\\\u + C\\ \\Voltando\; a\; sunstituicao\\\\u = arcsen(\frac{x}{7}) \\\\Resp = arcsen(\frac{x}{7}) + C$