\(\int \sin \sqrt{x}dx\)
Answer & explanation
Correct answer: option 1
$\int \sin \sqrt{x}dx$
let $x=t^2$ so $dx=2t\,dt$
$⇒I=2\int t\sin tdt=2(-t\cos t+\int\cos t dt)$
$=2(\sin t-t\cos t)+C$
$=2(\sin\sqrt{x}-\sqrt{x}\cos\sqrt{x})+C$
\(\int \sin \sqrt{x}dx\)
Correct answer: option 1
$\int \sin \sqrt{x}dx$
let $x=t^2$ so $dx=2t\,dt$
$⇒I=2\int t\sin tdt=2(-t\cos t+\int\cos t dt)$
$=2(\sin t-t\cos t)+C$
$=2(\sin\sqrt{x}-\sqrt{x}\cos\sqrt{x})+C$