Area Under Curves

Area bounded by curves

• Under a curve

  $A={\int }_a^b|f(x)|dx$or$A={\int }_c^d|g(y)|dy$

• Between two curves

  $A={\int }_a^b(f(x)-g(x))dx,$$f(x)\ge g(x)$on $[a,b]$

• Standard areas

  ellipse $\pi ab;$$y^2=4ax$and$x^2=4by:\frac{16ab}{3}$