5. Let f:[0,7]→R be defined by f(x)=x
2
−3x+1. Let α(x)=3I(x−1)+2I(x−4)+ I(x−5)+4I(x−6), where I is the unit step function. Compute ∫
0
7
​
fdα. (3 points)6. Prove: If \( \bar{f} \in \mathcal{R}(\alpha) \) on \( [a, b] \) and if \( aZILLDIFFEQMODAP11 4.2.002. The indicated function \( y_{1}(x) \) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, \[ y_{2}=y_{1}(x) \int \frac{(e^−∫P(x)dx /y1^2) * dx
as instructed, to find a second solution y
2
​
(x). y
′′
+2y
′
+y=0;y
1
​
=xe
−x
y
2
​
=