Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$e^{- x} \sin{\left(x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \pi$$
Numerical solution$$x_{1} = -18.8495559215388$$
$$x_{2} = -15.707963267949$$
$$x_{3} = 12.5663706143592$$
$$x_{4} = 3.14159265358979$$
$$x_{5} = -31.4159265358979$$
$$x_{6} = 84.8230016469244$$
$$x_{7} = 94.2477796076938$$
$$x_{8} = 21.9911485751286$$
$$x_{9} = 0$$
$$x_{10} = 81.6814089933346$$
$$x_{11} = 40.8407044966673$$
$$x_{12} = 62.8318530717959$$
$$x_{13} = 100.530964914873$$
$$x_{14} = -21.9911485751286$$
$$x_{15} = 47.1238898038469$$
$$x_{16} = 91.106186954104$$
$$x_{17} = 75.398223686155$$
$$x_{18} = 28.2743338823081$$
$$x_{19} = 34.5575191894877$$
$$x_{20} = 6.28318530717959$$
$$x_{21} = 78.5398163397448$$
$$x_{22} = 72.2566310325652$$
$$x_{23} = -6.28318530717959$$
$$x_{24} = 15.707963267949$$
$$x_{25} = 31.4159265358979$$
$$x_{26} = 106.814150222053$$
$$x_{27} = 25.1327412287183$$
$$x_{28} = 18.8495559215388$$
$$x_{29} = -3.14159265358979$$
$$x_{30} = 56.5486677646163$$
$$x_{31} = -25.1327412287183$$
$$x_{32} = 53.4070751110265$$
$$x_{33} = -28.2743338823081$$
$$x_{34} = -9.42477796076938$$
$$x_{35} = 87.9645943005142$$
$$x_{36} = 50.2654824574367$$
$$x_{37} = 69.1150383789755$$
$$x_{38} = 59.6902604182061$$
$$x_{39} = 97.3893722612836$$
$$x_{40} = -12.5663706143592$$
$$x_{41} = 37.6991118430775$$
$$x_{42} = 9.42477796076938$$
$$x_{43} = 65.9734457253857$$
$$x_{44} = -34.5575191894877$$
$$x_{45} = 43.9822971502571$$