Question

Very Quick!

Answer 1

\[\int\limits_{0}^{3}(\sqrt{2^x}\]

Answer 2

Do you mean
\[\large\int_0^3\sqrt{2^x}\,dx~~?\]

Answer 3

Yes, sorry keeping leaving stuff out :(

Answer 4

If that's the case, notice that
\[\large\sqrt{2^x}=\left(2^x\right)^{1/2}=2^{x/2}=\exp\left(\frac{x}{2}\ln2\right)\]
(If you're not familiar with notation, \(\exp(\cdots)\) means \(e^{\cdots}\).)

So,
\[\large\int_0^3\sqrt{2^x}\,dx=\int_0^3\exp\left(\frac{\ln2}{2}x\right)\,dx\]
Substitute \(u=\dfrac{\ln2}{2}x\).

Answer 5

Right! Thank you... again.
:)

Answer 6

yw!