Question

if the integral of : f(t) dt = 19 in the interval from [0,1]
then calculate the integral of : f(2t) dt in the interval [0,0.5]

Answer 1

i will guess
\[\frac{19}{2}\]

Answer 2

\[\int_0^1f(x)dx=19\] put
\[u=2x,du=\frac{1}{2}dx,\frac{1}{2}du=dx, u(0)=0,u(1)=.5\] then get
\[\frac{1}{2}\int_0^.5f(u)du\]