Subject : Applied Mathematics 2

Topic : Triple integration and Applications of Multiple integrals

Difficulty : Low

Consider a strip parallel to y-axis. On this strip y varies from y = 2 - x to 2 + x and x varies from 0 to 5.

$\text{Area} = \int^5_{x=0} \int^{2+x}_{y=2-x}dxdy$

$\hspace{0.9cm} = \int ^5_0 [y]^{2+x}_{2-x}dx$

$\hspace{0.9cm}= \int^5_0 ((2+x) - (2-x))dx$

$\hspace{0.9cm}= \int^5_0 2x dx$

$\hspace{0.9cm} = 2\big[\frac{x^2}{2}\big]^5_0 = 25$