Question 1

Evaluate each of the following integrals.

• $${\int_0^{10} t^2 e^{-t^3} \hspace{3pt}dt}$$.
  
  
  
  
  
  
  
  
  
  
  

• $${\int_0^{\frac{\pi}{6}} \cos(x)\sin^6(x) \hspace{3pt}dx}$$.
  
  
  
  
  
  
  
  
  
  
  
• $${\int_0^{\frac{\pi}{2}} x\sin(3x)\hspace{3pt} dx}$$.