Find the integral \(\int sin\frac{5}{2}x dx\)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{-2}{5}\cos {\frac{5}{2}}x+c$
Use substitution:
$t = \frac{5x}{2} \Rightarrow dt = \frac{5}{2}dx \Rightarrow dx = \frac{2}{5}dt$
$\int \sin \left( \frac{5x}{2} \right) dx = \int \sin t \cdot \frac{2}{5} dt$
$= \frac{2}{5} \int \sin t \, dt = \frac{2}{5} (-\cos t)$
$= -\frac{2}{5} \cos \left( \frac{5x}{2} \right) + C$