Question

integrate sin(sqrt(a*t)dt

Answer 1

i would start with a substitution. then use integration by parts

Answer 2

well, i have no idea how i can substitute here

Answer 3

is 'a' a constant?

Answer 4

\[u=\sqrt{at}\]

Answer 5

@syltan knock,knock

Answer 6

With the assumption that 'a' is a constant, make the u-substitution the way Zarkon did. That gives you:\[\bf \frac{ du }{ dx }=\frac{ a }{ 2\sqrt{at} } \implies dx = \frac{ 2\sqrt{at} }{ a }du\]So you get the integral:\[\bf \int\limits_{}^{}\frac{2\sqrt{at}\sin(u)}{a} \ du=\bf \frac{ 2 }{ a } \int\limits_{}^{}\sqrt{at}\sin(u) \ du\]Now use integrate by parts like Zarkon suggested to integrate the existing integral.
@syltan

Answer 7

I forgot to substitute \(\bf u\) for whereever there was \(\bf \sqrt{at}\). This is what the integral is supposed to to look like:\[\bf = \frac{ 2 }{ a }\int\limits_{}^{}usin(u) \ du\]Now use integration by parts.

Answer 8

The best thing to do would be to use tabular integration which is "integration by parts" except it's used when one function in the integrand can be differentiated to 0 while the othe r can be integrated infinitely. It's an easy way to do it.

Answer 9

ok i get the idea thx.