How do you evaluate the definite integral (6x24e2x)dx from [0,2]?

1 Answer
Jul 17, 2018

2(e49)91.1963

Explanation:

Given: 20(6x24e2x)dx

Break the integral into two pieces and solve separately:

206x2dx204e2xdx=

620x2dx420e2xdx

Integration rules:
Use the Power rule: xndx=1n+1xn+1+C

Use eudu=eu+C

Let u=2x; du=2dx; dx=du2
x=0,u=0; x=2u=4

Using the rules:
620x2dx420e2xdx=

613x320440eudu2=

2x320240eudu=

2(2)302eu40=

162(e4e0)=162(e41)=

162e4+2=182e4=

2(e49)91.1963