search
Log In
0 votes

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $F$ = $xi$ + $yj$+ $zk$ defined with respect to a Cartesian coordinate system having $i$, $j$ and $k$ as unit base vectors.

                                                                   $\iint_{s}^{ }\frac{1}{4}(F.n)dA$

where $S$ is the sphere, $x^2$ + $y^2$ + $z^2$ =$1$ and n is the outward unit normal vector to the sphere. The
value of the surface integral is

  1. $\pi$
  2. $2\pi$
  3. $3\pi/4$
  4. $4\pi$
in Calculus 1.4k points 4 7 17
recategorized by

Please log in or register to answer this question.

Answer:

Related questions

0 votes
0 answers
The surface integral $\displaystyle{} \int \int_{s}^{ }\dfrac{1}{\pi }(9xi-3yj)\cdot nds$ over the sphere given by $x^2+y^2+z^2=9$ is
asked Feb 24, 2017 in Calculus Arjun 24.6k points
0 votes
0 answers
A scalar potential $\varphi$ has the following gradient: $\bigtriangledown \varphi =yz\hat{i}+xz\hat{j}+xy\hat{k}$ . Consider the integral $\int_{c}^{ }\bigtriangledown \varphi .d\overrightarrow{r}$ on the curve $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$. The curve $C$ is ... . The value of the integral is ________
asked Feb 24, 2017 in Calculus Arjun 24.6k points
0 votes
0 answers
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to $0$ $\frac{-\pi }{4}$ $\frac{-\pi }{2}$ $\frac{\pi }{4}$
asked Feb 19, 2017 in Calculus Arjun 24.6k points
0 votes
0 answers
The value of the definite integral $\int_{1}^{e}\sqrt{x}\ln(x)dx$ is $\dfrac{4}{9}\sqrt{e^3}+\dfrac{2}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}-\dfrac{4}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}+\dfrac{4}{9}\\$ $\dfrac{4}{9}\sqrt{e^3}-\dfrac{2}{9}$
asked Feb 19, 2017 in Calculus piyag476 1.4k points
0 votes
0 answers
Choose the CORRECT set of functions, which are linearly dependent. $\sin x , \sin^2 x$ and $\cos^2 x$ $\cos x , \sin x$ and $\tan x$ $\cos 2x, \sin^2 x$ and $\cos^2 x$ $\cos 2x , \sin x$ and $cos x$
asked Feb 19, 2017 in Calculus piyag476 1.4k points
...