Sea y sea F $(x, y, z) = xi + yj + zk$, $S = \{(x, y, z) : x^2 + y^2 + z^2 = 1\} .$ Calcule la integral de superficie de F sobre S: $\iint_S F \cdot dS$
Added by Christopher C.
Close
Step 1
Since S is defined by the equation x + y = 1, we can rewrite it as y = 1 - x. Taking the partial derivatives with respect to x and y, we get ∂y/∂x = -1 and ∂y/∂y = 1. Therefore, the unit normal vector to S is N = <∂y/∂x, ∂y/∂y, -1> = <-1, 1, -1>. Show more…
Show all steps
Your feedback will help us improve your experience
Lucas Finney and 95 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Express the area of the given region as a sum of integrals of the form $\int_{a}^{b} f(x) d x$. The region enclosed by $y=|x|$ and $y=2-x^{2}$
The Integral
More on the Calculation of Area
Double integral over a general region Integrate the function f(x,y) = x^2 + y over the region D bounded by the lines y = x, x = 3 and y = -1. ∬D f(x, y)dA = ?
Israel H.
Evaluate ∬ₛ F ⋅ n dS if F = (x + y²)i - (2x)j + (2yz)k and S is the surface of the plane 2x + y + 2z = 6 in the first octant.
Sri K.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD