Multiple integrals

Concepts

• Double integral 10 exercisesThe double integral of a function f over a region D of the plane is the limit of the sums of the values of f times the area Delta…
• Fubini's theorem 10 exercisesIf f is continuous on a rectangle R=[a,b]×[c,d], its double integral with respect to the area A is computed as an iterated integr…
• Double integral over a general region 10 exercisesThe double integral of f with respect to the area A over a region D=\a≤ x≤ b,\ g_1(x)≤ y≤ g_2(x)\ is an iterated integral whose i…
• Triple integral 10 exercisesThe triple integral of a function f over a solid E of space is the limit of the sums of the values of f times the volume Delta V…
• Polar coordinates 10 exercisesPolar coordinates locate a point of the plane by its distance r from the origin and the angle θ its radius makes with the positiv…
• Cylindrical and spherical coordinates 10 exercisesCylindrical coordinates (r,θ,z) and spherical coordinates (rho,θ,φ) locate a point in space with distances and angles, and simpli…
• Change of variables in multiple integrals 10 exercisesA change of variables turns the integral of a function f over a region R of the xy-plane into one over a region S of the uv-plane…