Answer
See below
Work Step by Step
We are given: $f(t)=6t^2\\
g(t)=5t^3$
Obtain: $(f * g)=\int^t_0f(t-x)g(x)dx\\
=\int^t_06(t-x)^25x^3dx\\
=30\begin{vmatrix}
\frac{t^2x^4}{4}+\frac{x^6}{6}-\frac{2tx^5}{5}
\end{vmatrix}^t_0\\
=30(\frac{t^6}{4}+\frac{t^6}{6}-\frac{2t^6}{5})\\
=\frac{t^6}{2}$
