Question

The line integral of the vector function $\overrightarrow{F}=2x\hat{i}+x^2\hat{j}$ along the x - axis from x = 1 to x = 2 is

• A. 2.33
• B. 3
• C. 5.33

Answer 1

The correct option is B 3

Line integral is
${\int }_c\overrightarrow{f}.d\hat{r}$
$=\int (2x\hat{i}+x^2\hat{j}).(dx\hat{i}+dy\hat{j})$
$={\int }_c(2xdx+x^{2}dy)$
$={\int }_{x=1}^2\left(2xdx\right)$
$[\because$ along x axis; y = 0 $\Rightarrow$ dy = 0]
=3