Problems

01

Area between curves: integrating in $x$

Compute the area enclosed between the given curves:

• (a) Between $y=6x$ and $y=x^3-10x$. (Hint: watch out: which is on top where?)
  [Note: original first function was $y=3x+8$; solutions with this one are also valid.]
• (b) Above $y=x$, below-right of $y=8x$, below-left of $y=\frac{8}{x^2}$. (Hint: divide into 2 integrals.)
• (c) Find the area of the shaded region:
  

02

Area between curves: integrating in $y$

Compute the area enclosed between the given two curves:

• (a) $x=y^2-1$ and $x=-\frac{1}{8}{y}^4+y^2+1$
  
• (b) $x=y^3-26y+10$ and $x=-y^3-6y^2+40$