Study guide and
1 practice problem
on:
Ways of computing a double integral
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There are multiple ways of computing the double integral $\iint_D f(x,y) \ dA$:
Express the double integral as two iterated integrals: $$\int_a^b \int_{g(x)}^{h(x)} f(x,y) dy dx$$
Use Green's Theorem to convert the double integral into a line integral.
Related topics
Double integrals
(3 problems)
Multivariable calculus
(147 problems)
Practice problem
Let $\rho(r,\theta) = 1/r$ and let $R$ be the cardioid given by $r=a(1+\cos \theta)$ for positive $a$. Evaluate $$ \iint_R \rho \ dA.$$
Solution