Free Printable Double Integral

1.

$\int\int x^2dydx$

a)

$x^3y^3+C$

b)

$\frac{1}{3}x^3y^3+C$

c)

$\frac{1}{3}xy^3+C$

d)

$\frac{1}{3}x^3y+C$

2.

$\int\int\left(y-z\right)dxdy$

a)

$\frac{1}{2}xy^2-xyz+C$

b)

$\frac{1}{2}xy^2+xyz+C$

c)

$\frac{1}{2}x^2y^{ }-xyz+C$

d)

$\frac{1}{2}xy^2-x^2yz+C$

3.

$\int\int\left(3x^2+2y\right)dxdy$

a)

$xy\left(y^2+x\right)+C$

b)

$xy\left(x^2+y\right)+C$

c)

$x^3y^2+xy^2+C$

d)

$x^2y^3+xy+C$

4.

$\int_1^2\int_3^4\left(2x-7y\right)dxdy$

a)

3.50

b)

-3.50

c)

1.50

d)

-1.50

5.

$\int_{-3}^5\ \int_5^{-3}\ x^2y^2\ dxdy$

a)

$\approx-2,\ 567$

b)

$\approx1,\ 890$

c)

$\approx4,\ 215$

d)

$\approx1,941$

6.

$\int_2^9\int_5^8\ \left(\sin\ 2x\right)dxdy$

a)

$\approx0.792$

b)

$\approx0.518$

c)

$\approx-0.231$

d)

$\approx0.415$

7.

Curves $x^2=2-y$ and $x=y$ are shown in this figure. Set up a double integral to find the area of the blue region.

a)

$\int_{-2}^1\int_x^{x^2}1\ dydx$

b)

$\int_x^2\int_1^21\ dydx$

c)

$\int_{-2}^1\int_x^{\left(2-x^2\right)}1\ dydx$

d)

$\int_{-2}^0\int_y^{\left(2-y\right)}1\ dxdy$

8.

The base of a solid is the blue region which is a quarter of the circle $x^2+y^2=64$ . If the volume of the solid is given by $\int_0^8\int_0^mf\left(x,y\right)\ dydx$ , find m.

a)

8

b)

$\sqrt{x^2-64}$

c)

$\sqrt{8-x^2}$

d)

$\sqrt{64-x^2}$

9.

A cheese with width = 5cm, length = 10cm and height = 5cm is placed at the origin of xyz axes as shown in the figure. Set up a double integral to determine the volume of the cheese.

a)

$\int_0^{10}\int_0^{\frac{y}{2}}5\ dxdy$

b)

$\int_0^5\int_0^{2x}1\ dydx$

c)

$\int_0^{10}\int_0^55\ dxdy$

d)

$\int_0^5\int_0^52x\ dydx$

10.

The base of a solid is the blue region which is a quarter of the circle $x^2+y^2=64$ . If the volume of the solid is given by $\int_0^8\int_0^mf\left(x,y\right)\ dydx$ , find m.

a)

8

b)

$\sqrt{x^2-64}$

c)

$\sqrt{8-x^2}$

d)

$\sqrt{64-x^2}$

Double Integral

Total questions: 10

Worksheet time: 5mins

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