Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$e^{- x} \sin{\left(2 x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{2}$$
Numerical solution$$x_{1} = 72.2566310325652$$
$$x_{2} = 94.2477796076938$$
$$x_{3} = -3.14159265358979$$
$$x_{4} = 36.1283155162826$$
$$x_{5} = 40.8407044966673$$
$$x_{6} = 98.9601685880785$$
$$x_{7} = -15.707963267949$$
$$x_{8} = -31.4159265358979$$
$$x_{9} = 6.28318530717959$$
$$x_{10} = 62.8318530717959$$
$$x_{11} = 81.6814089933346$$
$$x_{12} = 100.530964914873$$
$$x_{13} = 48.6946861306418$$
$$x_{14} = 50.2654824574367$$
$$x_{15} = 84.8230016469244$$
$$x_{16} = -17.2787595947439$$
$$x_{17} = 61.261056745001$$
$$x_{18} = -9.42477796076938$$
$$x_{19} = 76.9690200129499$$
$$x_{20} = -1.5707963267949$$
$$x_{21} = 15.707963267949$$
$$x_{22} = 97.3893722612836$$
$$x_{23} = 73.8274273593601$$
$$x_{24} = 51.8362787842316$$
$$x_{25} = 78.5398163397448$$
$$x_{26} = -6.28318530717959$$
$$x_{27} = 12.5663706143592$$
$$x_{28} = -23.5619449019235$$
$$x_{29} = 70.6858347057703$$
$$x_{30} = 58.1194640914112$$
$$x_{31} = 56.5486677646163$$
$$x_{32} = -28.2743338823081$$
$$x_{33} = 18.8495559215388$$
$$x_{34} = 7.85398163397448$$
$$x_{35} = 59.6902604182061$$
$$x_{36} = -25.1327412287183$$
$$x_{37} = -21.9911485751286$$
$$x_{38} = 86.3937979737193$$
$$x_{39} = 10.9955742875643$$
$$x_{40} = -7.85398163397448$$
$$x_{41} = 92.6769832808989$$
$$x_{42} = 80.1106126665397$$
$$x_{43} = 43.9822971502571$$
$$x_{44} = 28.2743338823081$$
$$x_{45} = 4.71238898038469$$
$$x_{46} = 32.9867228626928$$
$$x_{47} = 20.4203522483337$$
$$x_{48} = 64.4026493985908$$
$$x_{49} = 42.4115008234622$$
$$x_{50} = 65.9734457253857$$
$$x_{51} = -14.1371669411541$$
$$x_{52} = 26.7035375555132$$
$$x_{53} = 34.5575191894877$$
$$x_{54} = 95.8185759344887$$
$$x_{55} = 0$$
$$x_{56} = 14.1371669411541$$
$$x_{57} = 54.9778714378214$$
$$x_{58} = 21.9911485751286$$
$$x_{59} = 87.9645943005142$$
$$x_{60} = 37.6991118430775$$
$$x_{61} = -29.845130209103$$
$$x_{62} = 29.845130209103$$