Question

Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 0 0 12 dy dx -1 -?1-x² 1+?x² + y² 2 Change the Cartesian integral into an equivalent polar integral. 0 0 12 -1 -?1-x² 1+?x² + y² dy dx = ? ? dr d? ? 0 (Type exact answers, using ? as needed.) The value of the double integral is (Type an exact answer, using ? as needed.)

          Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.
0
0
12
dy dx
-1 -?1-x²
1+?x² + y²
2
Change the Cartesian integral into an equivalent polar integral.
0
0
12
-1 -?1-x²
1+?x² + y²
dy dx = ? ? dr d?
? 0
(Type exact answers, using ? as needed.)
The value of the double integral is 
(Type an exact answer, using ? as needed.)

Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.
0
0
12
dy dx
-1 -?1-x²
1+?x² + y²
2
Change the Cartesian integral into an equivalent polar integral.
0
0
12
-1 -?1-x²
1+?x² + y²
dy dx = ? ? dr d?
? 0
(Type exact answers, using ? as needed.)
The value of the double integral is
(Type an exact answer, using ? as needed.)

Added by Kyle E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Kyle Sower

08/17/2022

Step 1

Step 1: To change the Cartesian integral into an equivalent polar integral, we need to convert the limits of integration and the differential elements. Show more…

Show all steps

Thanks for your feedback!

Change the Cartesian integral into an equivalent polar integral. int_{-1}^{0} int_{-sqrt{1-x^{2}}}^{0} frac{12}{1+sqrt{x^{2}+y^{2}}} dy dx = int_{pi}^{ heta} int_{0}^{ heta} dr d heta (Type exact answers, using pi as needed.) The value of the double integral is (Type an exact answer, using pi as needed.) Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral int_{0}^{0} 12 dy dx frac{1}{x^{2}+sqrt{1-x^{2}}} Change the Cartesian integral into an equivalent polar integral int_{0}^{0} 12 dy dx = int_{0}^{0} dr d heta frac{1-x^{2}}{t} (Type exact answers, using t as needed.) The value of the double integral is Type an exact answer, using t as needed.