Linear algebra question

[hank]

I'm getting the answer of -1/14, but the book says zero.
Is the book correct?

Here's my work:

Compute <f,g> where f(t) = 1 - 3t^2 and g(t) = t - t^3
f(t)g(t) = t - 4t^3 + 3t^6

S[0 - 1] (t - 4t^3 + 3t^6) dt
= (1/2)t^2 - t^4 + (3/7)t^7 | [1,0]
= 1/2 - 1 + 3/7
= 7/14 - 14/14 + 6/14
= -1/14

 

[pka]

You have multiplied incorrectly.
\(\displaystyle f(t)g(t) = t - 4t^3 + 3t^5\)