In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 17. ∫ − 1 0 ∫ − 1 − x 2 0 2 1 + x 2 + y 2 d y d x
In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 17. ∫ − 1 0 ∫ − 1 − x 2 0 2 1 + x 2 + y 2 d y d x
In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.
17.
∫
−
1
0
∫
−
1
−
x
2
0
2
1
+
x
2
+
y
2
d
y
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Evaluate
| exp(-2²)dx,
using
an iterated integral and polar coordinates.
Find the integral
fhpæp(z+6)/(z-6)
by transforming to polar coordinates.
I =
%3D
Example6:
Change the Cartesian integral into equivalent polar integral, then evaluate the polar integral
xdxdy
Sol:
dydx = rdrde
"4 r2csce
"/4
r2 cos 0 drd0 =
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY