GATE (TF) Textile 2008 Question Paper Solution | GATE/2008/TF/24

Question 24 (Textile Engineering & Fibre Science)

A curve in space is represented by a vector $\vec{r}(t)=x(t)i+y(t)j+z(t)k$ . Given a vector function $\vec{F}(\vec r)=5z\;i+xy\;j+x^2z\;k$ and $\vec{r}(t) = ti+tj+tk$ , $0\leq t\leq 1$ , the value of the integral

$\int_{0}^{1}[\vec F(\vec r(t)).\frac{d\vec r}{dt}]dt$

(A)	$\frac{7}{12}$
(B)	$\frac{17}{12}$
(C)	$\frac{27}{12}$
(D)	$\frac{37}{12}$

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