Recent questions tagged integral-analysis-for-a-control-volume

Let $C$ be the circle $(x-1)^{2}+y^{2}=25$ oriented counterclockwise. Then, the value of the line integral$$\oint_{C}\left[\left(x^{5}-3 y\right) d x+\left(-2 x+e^{y^{2}}...

Let $L$ be the lamina of the form $x^{2}+4 y^{2} \leq 64,0 \leq y \leq 4$, with density $\rho(x, y)=\mid x \mid y$. Then, the mass of $L$ (in integer) is $\_\_\_\_$

​​​Statement of Reynolds Transport Theorem is given below with three blanks.The rate of change of $\_\_\_\_\_$ extensive property can be calculated by summing the rate of...

A fixed control volume has four one-dimensional boundary sections $(1,2,3$, and $4$). For a steady flow inside the control volume, the flow properties at each section are...

If\[\int_{0}^{\alpha} \int_{\sqrt{x / \alpha}}^{1} e^{y^{3}} d y d x=e-1, \quad \alpha>0,\]then the value $\text{(in integer)}$ of $\alpha$ is __________.

If the quadrature formula $\int_{-1}^{1} f(x) d x \approx \frac{1}{9}\left(c_{1} f(-1)+c_{2} f\left(\frac{1}{2}\right)+c_{3} f(1)\right)$is exact for all polynomials of d...

Let $\Gamma$ be the positively oriented circle $x^2+y^2=9$ in the $x y$-plane. If$$\oint_{\Gamma}\left(3 y+e^{x \sin x}\right) d x+\left(7 x+\sqrt{e^y+2}\right) d y=\alph...

Let $f:(0, \infty) \rightarrow \mathbb{R}$ be the continuous function such that $f(x)=2+\frac{g(x)}{x}$ for all $x>0$, where $g(x)=\int_{1}^{x} f(t) d t$ for all $x>0$. T...