Consider a force `overset ( r)(F)= -x^(3) hat( i) +y^(2) hat(j) `.The work done by this force in moving a particle from A(1,0) to B(0,1) along a straight line is `:` ( All quantities are in SI units )

Options

A. 1
B. `(5)/(12)`
C. `( 7)/( 12) `
D. `( 3)/( 4)`

Explanation

To solve the problem of calculating the work done by the force \( \overset{\rightarrow}{F} = -x^3 \hat{i} + y^2 \hat{j} \) while moving a particle from point A(1,0) to point B(0,1) along a straight line, we will follow these steps:

### Step 1: Understand the Work Done Formula
The work done \( W \) by a force along a path is given by the line integral:
\[ W = \int_C \overset{\rightarrow}{F} \cdot d\overset{\rightarrow}{s} \]
where \( C \) is the path from point A to point B, and \( d\overset{\rightarrow}{s} \) is the differential displacement vector along the path.
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