Applied Calculus: UNIT IV: Multiple Integrals
Double integrals in Polar coordinates
Explanation, Formula, Equation, Example and Solved Problems - Multiple Integrals (Iterated Integrals) : Double integrals in Polar coordinates
DOUBLE
INTEGRALS IN POLAR COORDINATES
Consider the integral
which is in the polar
form. This integral is bounded over the region by the straight line θ1,
θ = θ2 and the curves r = r1, r = r2. To
evaluates the integral, we first integrate with respect to r between the limits r = r1 and r = r2
(treating θ as a constant). The resulting expression is then integrated with
respect to θ between θ = θ1, and θ = θ2.
Geometrically, PQ and
RS are the curves r = f1(θ) and r = f2(θ)
bounded by the lines θ = θ1 and θ = θ2 so that PRSQ is
the region of integration. AB is wedge of angular thickness δθ. Then
indicates that the
integration is performed along AB (i.e., r varies, θ constant) and the
integration with respect to θ
means rotation of this
strip AB from PR to QS.
EXERCISE
Applied Calculus: UNIT IV: Multiple Integrals : Tag: Applied Calculus : - Double integrals in Polar coordinates
Applied Calculus: UNIT IV: Multiple Integrals
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Applied Calculus
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