12.2: Iterated Integrals

Question 1

(integral b-a) (integral d-c) f(x,y) dy dx

Answer 1

• do integral d-c first and in respect to y
• do integral b-a last in respect to x

Question 2

Fabini’s Theorem

Answer 2

(integral b-a) (integral d-c) f(x,y) dy dx = (integral d-c) (integral b-a) f(x,y) dx dy as long as f(x,y) is continuous and your region is rectangular, R=[a,b]x[c,d]

Question 3

Separable Theorem

Answer 3

If f(x,y) = g(x) h(y) over a rectangular region, R= [a,b]x[c,d] then you double integral can be viewed as a product of 2 single integrals
- (integral b-a) (integral d-c) f(x,y) dy dx = ( (integral d-c) f(x,y) dy) X ((integral b-a) f(x,y) dx)