Question

suppose S (0 to 1) f(t)dt =3 calculate the following:

Answer 1

\[\int\limits_{0}^{1}f(t)dt=3 calculate the following: \]

Answer 2

\[\int\limits_{0}^{.5}f(2t)dt\]

Answer 3

f(x)=1/(x+1) vs f(2x)=1(2x+1)
f(x)=x^2 vs f(2x)=4x^2

Can you make any comparison to functions you can easily find the integral of to determine some pattern?

Answer 4

they are similar

Answer 5

\[\int\limits_{2a}^{2b}f(2t)dt=\frac{ 1 }{ 2 } \int\limits_{a}^{b}f(u)du=\frac{ 1 }{ 2 } \int\limits_{a}^{b}f(t)dt\]
\[\int\limits_{0}^{0.5}f(2t)dt=\frac{ 1 }{ 2 } \int\limits_{0}^{2}f(u)du=\frac{ 1 }{ 2 } \int\limits_{0}^{2}f(t)dt=\frac{3}{2}\]

Answer 6

because by get u=2t we have
du=2 dt