求定积分 f上限1,下线0(3^x+根号x)dx
问题描述:
求定积分 f上限1,下线0(3^x+根号x)dx
答
=(3^x)/(ln3)+2/3*x^(3/2)代入上下限,得到2/(ln3)+2/3
答
∫ (3^x +根号x)dx
=∫3^xdx +∫(根号x)dx
=∫d(3^x)/ln3 + ∫ 2/3d x^(3/2)
=3^x/ln3 +2/3x^(3/2)+C
带入0 1
得到原式= 3/ln3+2/3×+C- 1/ln3 +C
=2/ln3 +2/3 -1/ln3
=2/ln3+2/3