← Double & Triple Integrals

Practice: Multiple Integrals

8 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

\iint_{R} y d A

over

R = [0, 1] \times [0, 2]

equals

Q2.

intermediateTest 2 Review #46 style

True/False:

\int_{a}^{b} \int_{c}^{d} f (x) g (y) d y d x = (\int_{a}^{b} f (x) d x) (\int_{c}^{d} g (y) d y)

.

Q3.

basic

If

D

is the triangle with vertices

(0, 0), (1, 0), (0, 1)

, then

\iint_{D} 1 d A =

Q4.

intermediate

Volume bounded by

z = 4 - x^{2} - y^{2}

and the

x y

-plane equals

Q5.

basic

\int_{0}^{1} \int_{0}^{x^{2}} y d y d x =

Q6.

basic

True/False: For continuous

f

on a rectangle,

\int_{a}^{b} \int_{c}^{d} f (x, y) d y d x = \int_{c}^{d} \int_{a}^{b} f (x, y) d x d y

.

Q7.

intermediate

Mass of the disk

x^{2} + y^{2} \leq 1

with density

ρ (x, y) = x^{2} + y^{2}

equals

Q8.

intermediate

Average value of

f (x, y) = x y

over

[0, 2] \times [0, 3]

is