Answer
a) b and b) b
Work Step by Step
a) Average value can be calculated as: $\dfrac{1}{2} \int_{-1}^1 (mx+b ) dx$
$=\dfrac{1}{2} [mx^2/2+bx]_{-1}^1$
or, $\dfrac{1}{2} [m(1/2-1/2)+b(1+1)]=b$
b) Average value can be calculated as: $\dfrac{1}{2k} \int_{-k}^k (mx+b ) dx$
$=\dfrac{1}{2k} [mx^2/2+bx]_{-k}^k1$
or, $\dfrac{1}{2k} [m(k/2-k/2)+b(k+k)]=b$
Hence, a) b and b) b
