Question

DAU COROANA!!!Aflati integrala functiei radical din x dx,faca f(x) trece prin puncul M(1,-3)

Answer 1

F(x)=$\int\limits { \sqrt{x} } \, dx = \int\limits { x^{ \frac{1}{2} } } \, dx= \frac{x^ \frac{1}{2}+1 }{ \frac{1}{2}+1 }+C= \frac{2}{3} x^{ \frac{3}{2} } +C$, determinam constanta C astfel ca F(1)=-3, adica 2/3*1+C=-3, deci C=-11/3, integrala va fi F(x)=$\frac{2}{3} \sqrt{x^3} - \frac{11}{3}$