Which of the following double integrals in polar coordinates is equivalent to $ \mathop \smallint \limits_0^\infty \mathop \smallint \limits_0^\infty e^{-(x^2+y^2)} dx~dy$ ?

Question

Which of the following double integrals in polar coordinates is equivalent to $ \mathop \smallint \limits_0^\infty \mathop \smallint \limits_0^\infty e^{-(x^2+y^2)} dx~dy$ ?

TuteeHUB · Accepted Answer

$ \mathop \smallint \limits_0^{2\pi} \mathop \smallint \limits_0^\infty e^{-r^2} dr~d\theta$

TuteeHUB · Answer

$ \mathop \smallint \limits_0^\frac{\pi}{2} \mathop \smallint \limits_0^\infty e^{-r^2} dr~d\theta$

TuteeHUB · Answer

$ \mathop \smallint \limits_0^\frac{\pi}{2} \mathop \smallint \limits_0^\infty e^{-r^2} r~ dr~d\theta$

TuteeHUB · Answer

$ \mathop \smallint \limits_0^{2\pi} \mathop \smallint \limits_0^\infty e^{-r^2} r~dr~d\theta$

1.	Which of the following double integrals in polar coordinates is equivalent to \( \mathop \smallint \limits_0^\infty \mathop \smallint \limits_0^\infty e^{-(x^2+y^2)} dx~dy\) ?
A.	\( \mathop \smallint \limits_0^\frac{\pi}{2} \mathop \smallint \limits_0^\infty e^{-r^2} dr~d\theta\)
B.	\( \mathop \smallint \limits_0^\frac{\pi}{2} \mathop \smallint \limits_0^\infty e^{-r^2} r~ dr~d\theta\)
C.	\( \mathop \smallint \limits_0^{2\pi} \mathop \smallint \limits_0^\infty e^{-r^2} dr~d\theta\)
D.	\( \mathop \smallint \limits_0^{2\pi} \mathop \smallint \limits_0^\infty e^{-r^2} r~dr~d\theta\)
Answer» C. \( \mathop \smallint \limits_0^{2\pi} \mathop \smallint \limits_0^\infty e^{-r^2} dr~d\theta\)

Which of the following double integrals in polar coordinates is equivalent to \( \mathop \smallint \limits_0^\infty \mathop \smallint \limits_0^\infty e^{-(x^2+y^2)} dx~dy\) ?

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