You need to use the substitution `0.2y = u` , such that:
`0.2y= u => 0.2dy = du => dy= (du)/(0.2)`
Replacing the variable, yields:
`int y*e^(0.2y) dy = (10/2)int u/(0.2)*e^u du`
You need to use the integration by parts such that:
`int fdg = fg - int gdf`
`f = u => df = du`
`dg = e^u=> g = e^u`
2`5int u*e^u du = 25(u*e^u - int e^u du)`
`25int u*e^u du = 25u*e^u - 25e^u + c`
Replacing back the variable, yields:
`int y*e^(0.2) dy = 25((0.2y)*e^(0.2y) - e^(0.2y)) + c`
Hence, evaluating the integral, using substitution, then integration by parts, yields `int y*e^(0.2) dy = ((e^(0.2y))/9)(0.2y - 1) + c`
No comments:
Post a Comment