Question

Evaluate the iterated integral after changing coordinates systems. Enter an exact asswer. Do mot ese a decimal appresimation. \int_0^7 \int_(-\sqrt(49-y^(2)))^(\sqrt(49-y^(2))) \int_(\sqrt(x^(2) y^(2)))^(\sqrt(98-x^(2)-y^(2))) 2dxdxdy= $$\int_{0}^{7} \int_{-\sqrt{49-y^2}}^{\sqrt{49-y^2}} \int_{\sqrt{x^2+y^2}}^{\sqrt{98-x^2-y^2}} 2 dz dx dy$$

Name: evaluate the iterated integral after changing coordinates systems enter an exact asswer do mot ese a decimal appresimation int07 int sqrt49 y2sqrt49 y2 intsqrtx2 y2sqrt98 x2 y2 2dxdxdy in 69678
Uploaded: 2020-09-08T04:10:28-08:00
Duration: 2 min 16 s
Channel: Jack Chen
Description: evaluate the iterated integral after changing coordinates systems enter an exact asswer do mot ese a decimal appresimation int07 int sqrt49 y2sqrt49 y2 intsqrtx2 y2sqrt98 x2 y2 2dxdxdy in 69678

          Evaluate the iterated integral after changing coordinates systems. Enter an exact asswer. Do mot ese a decimal appresimation.
\int_0^7 \int_(-\sqrt(49-y^(2)))^(\sqrt(49-y^(2))) \int_(\sqrt(x^(2) y^(2)))^(\sqrt(98-x^(2)-y^(2))) 2dxdxdy=
$$\int_{0}^{7} \int_{-\sqrt{49-y^2}}^{\sqrt{49-y^2}} \int_{\sqrt{x^2+y^2}}^{\sqrt{98-x^2-y^2}} 2 dz dx dy$$

evaluate the iterated integral after changing coordinates systems enter an exact asswer do mot ese a decimal appresimation int07 int sqrt49 y2sqrt49 y2 intsqrtx2 y2sqrt98 x2 y2 2dxdxdy in 69678

Added by Bryan Z.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Jack Chen

09/08/2020

Step 1

$x = r\cos\theta$, $y = r\sin\theta$, $z = z$. $x^2 + y^2 = r^2$. The Jacobian is $r$. The limits of integration are: $0 \le y \le 7$, $-\sqrt{49-y^2} \le x \le \sqrt{49-y^2}$. This describes the region $x^2 + y^2 \le 49$ with $y \ge 0$. In polar coordinates, this Show more…

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Evaluate the iterated integral after changing coordinates systems. Enter an exact asswer. Do mot ese a decimal appresimation. \int_0^7 \int_(-\sqrt(49-y^(2)))^(\sqrt(49-y^(2))) \int_(\sqrt(x^(2) y^(2)))^(\sqrt(98-x^(2)-y^(2))) 2dxdxdy= $$\int_{0}^{7} \int_{-\sqrt{49-y^2}}^{\sqrt{49-y^2}} \int_{\sqrt{x^2+y^2}}^{\sqrt{98-x^2-y^2}} 2 dz dx dy$$