Average value of integral

[wassupman]

Can anyone wal me through the steps for this? I set the equation so I solved for a and b but i get values that are not even close to correct.

 

[skeeter]

[MATH]1 \bigg[\dfrac{x^3}{3} + \dfrac{ax^2}{2} +bx \bigg]_0^1 = \dfrac{1}{3} + \dfrac{a}{2} + b = \dfrac{49}{3} \implies \dfrac{a}{2}+b = 16[/MATH]
[MATH]\dfrac{1}{4}\bigg[\dfrac{x^3}{3} + \dfrac{ax^2}{2} +bx \bigg]_0^4 = \dfrac{82}{3} \implies \dfrac{16}{3}+ 2a + b = \dfrac{82}{3}[/MATH]
solve the system of equations

 

[wassupman]

Ahh I see, thank you for the help skeeter