Consider a vector field $$\overrightarrow {\text{A}} \left( {\overrightarrow {\text{r}} } \right).$$ The closed loop line integral $$\oint {\overrightarrow {\text{A}} \cdot \overrightarrow {{\text{d}}l} } $$ can be expressed as
A. $$\mathop{{\int\!\!\!\!\!\int}\mkern-21mu \bigcirc} {\left( {\nabla \times \overrightarrow {\text{A}} } \right) \cdot \overrightarrow {{\text{ds}}} } $$ over the closed surface bounded by the loop
B. $$\mathop{{\int\!\!\!\!\!\int\!\!\!\!\!\int}\mkern-31.2mu \bigodot} {\left( {\nabla \cdot \overrightarrow {\text{A}} } \right){\text{dv}}} $$ over the closed volume bounded by the top
C. $$\iiint {\left( {\nabla \cdot \overrightarrow {\text{A}} } \right){\text{dv}}}$$ over the open volume bounded by the loop
D. $$\iint {\left( {\nabla \times \overrightarrow {\text{A}} } \right) \cdot \overrightarrow {{\text{ds}}} }$$ over the open surface bounded by the loop
Answer: Option D
This Question Belongs to Engineering Maths >> Calculus
The Taylor series expansion of 3 sinx + 2 cosx is . . . . . . . .
A. 2 + 3x - x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
B. 2 - 3x + x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
C. 2 + 3x + x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
D. 2 - 3x - x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
B. \[\infty \]
C. \[\frac{1}{2}\]
D. \[ - \infty \]
A. \[1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
B. \[ - 1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
C. \[1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
D. \[ - 1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
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