Cheat Sheet – Area under Curves
DOUBLEROOT
Area bounded by y = f(x), y = 0, x = a, x = b
Area bounded by x = f(y), x = 0, y = a, y = b
b
A = ∫ f(y)dy
a
b
A = ∫ f(x)dx
a
Area bounded by x = f(y), x = 0
Area bounded by y = f(x), y = 0
b
c
A = ∫ f(y)dy − ∫ f(y)dy
a
b
where a,b,c are the roots of f(y) = 0
b
c
A = ∫ f(x)dx − ∫ f(x)dx
a
b
where a,b,c are the roots of f(x) = 0
Area bounded by y = f(x), y = g(x), x = a, x = b
Area bounded by x = f(y), x = g(y), y = a, y = b
b
A = ∫ (f(y) − g(y))dy
a
b
A = ∫ (f(x) − g(x))dx
a
Area bounded by y = f(x), y = g(x)
Area bounded by x = f(y), x = g(y)
b
A = ∫ f(y) − g(y)dy
a
c
− ∫ g(y) − f(y)dy
b
where a,b,c are the roots of f(y) = g(y)
b
c
A = ∫ f(x) − g(x)dx − ∫ g(x) − f(x)dx
a
b
where a,b,c are the roots of f(x) = g(x)
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