在区间[0,1]里 求∫x^3dx=?求∫x^4＝?求∫e^xdx=?求∫e^5x=?

题目

在区间[0,1]里 求∫x^3dx=?求∫x^4＝?求∫e^xdx=?求∫e^5x=?

答案

∫x^3dx= 1/4*x^4 +C
∫[0,1] x^3dx = 1/4*x^4 |[0,1] =1/4
∫x^4dx= 1/5*x^5 +C
∫[0,1] x^4dx = 1/5*x^5 |[0,1] =1/5
∫e^xdx= e^x +C
∫[0,1] e^xdx= e^x|[0,1] =e-1
∫e^5xdx = 1/5∫e^5xd5x = 1/5*e^5x +C
∫[0,1] e^5xdx = 1/5*e^5x|[0,1] = 1/5*e^5 -1/5