Paul Lawson
03/14/2023 · Primary School
Let \( \mathbf{n} \) be the outer unit normal of the elliptical shell \( S: 36 x^{2}+25 y^{2}+900 z^{2}=900, z \geq 0 \), and let \( \mathbf{F}=\mathrm{yi}+\mathrm{x}^{2} \mathbf{j}+\left(\mathrm{x}^{2}+\mathrm{y}^{4}\right)^{3 / 2} \sin e^{\sqrt{x y z}} \mathbf{k} \). Find the value of \( \iint_{S}(\nabla \times \mathbf{F}) \cdot \mathbf{n} d \sigma \). (Hint: One parameterization of the ellipse at the base of the shell is \( x=5 \cos t, y=6 \sin t, 0 \leq t \leq 2 \pi \).) \( \iint_{S}(\nabla \times \mathbf{F}) \cdot \mathbf{n} \) do \( =\square \) (Type an exact answer, using \( \pi \) as needed.)
UpStudy ThothAI Solution
Tutor-Verified Answer
Quick Answer
The value of the surface integral is \(-30\pi\).
Step-by-step Solution
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit