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A double integral sums a function f(x,y)
over a two-dimensional region R
, giving, for example, the volume under a surface. For circular regions, switching to polar coordinates can simplify your work.
The general form is:
In rectangular coordinates:
In polar coordinates (,; Jacobian = ):
Step 1: Identify f(x,y)
and region R
; choose rectangular or polar coordinates.
Step 2: Write down the iterated integral with correct limits.
Step 3: Integrate the inner integral first, then the outer.
Step 4: Simplify and evaluate.
Example: over the unit disk
Switching to polar coordinates:
Tips & Tricks
polar coordinates
for circular regions—remember the Jacobian.R
to determine limits easily.TRY FREE NOW, no sign-up required: Double Integral Calculator from AI School Solutions gives you accurate & step-by-step solutions!
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