Question

Вычислить несобственный интеграл

Answer 1

$\ int_{0}^{1}{arcsin{x}oversqrt{1-x^2}}mathrm dx=|u=arcsin{x},sqrt{1-x^2}du=dx|=int_{0}^{1}umathrm du={1over2}u^2|_{0}^{1}={arcsin^2{x}over2}|_{0}^{1}={1over2}(arcsin^2{1}-arcsin^2{0})={1over2}cdot{pi^2over4}={pi^2over8}$