Double Integration over General Regions

Practice Questions

Calculus 3 › Double Integration over General Regions

Page 1 of 3

10 of 22

1

Calculate the following Integral.

$\int_{0}^{1}\int_{x}^{x^2} xy^2 dydx$

2

Evaluate the following integral on the region specified:

$\int\int_R(x^3y):dxdy$

Where R is the region defined by the conditions:

$0\leq x \leq 2, ; 1\leq y \leq2$

3

Calculate the following Integral.

$\int_{0}^{1}\int_{x}^{x^2} xy^2 dydx$

4

Evaluate the double integral

$\int_0^2 \int_0^1 y-2x,dx,dy$

5

Evaluate the integral $\int_{1}^{3}\int_{0}^{2}(xy^3)dxdy$

6

Calculate the definite integral of the function , given below as

$f(x,y)= 3x^3\sqrt{y}+ \sin(2x)\cos(4y)$

7

Evaluate the following integral.

$\int_{0}^{1}\int_{2}^{3}\left (5x^4y \right )dydx$

8

Evaluate the following integral: $\int_{0}^{1}\int_{3}^{6}(6x^2z)dzdx$

9

Evaluate the following iterated integrals:

$\int_-_1^3 \int_0^\frac{\pi}{2} y^2 \cos(x) \ dxdy$

10

Evaluate:

$\int_{1}^{3}\int_{y}^{2y}dxdy$

Page 1 of 3

Return to subject