An object is displaced from positin vector `r_1=(2hati+3hatj)` m to `r_2=(4hati+6hatj)` m under a forc `F=(3x^2hati+2yhatj)N` Find the work done by this force.

Explanation

To find the work done by the force \( \mathbf{F} = (3x^2 \hat{i} + 2y \hat{j}) \) as an object is displaced from position vector \( \mathbf{r_1} = (2 \hat{i} + 3 \hat{j}) \) m to \( \mathbf{r_2} = (4 \hat{i} + 6 \hat{j}) \) m, we will follow these steps:

### Step 1: Define the Work Done Formula
The work done by a force along a path can be calculated using the integral:
\[ W = \int_{\mathbf{r_1}}^{\mathbf{r_2}} \mathbf{F} \cdot d\mathbf{r} \]
where \( d\mathbf{r} = dx \hat{i} + dy \hat{j} \).
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