Mathematics I20745 marksNumerical: arc lengthArc length
Find the length f the arc of the semicubical y2 = x2 between the points (1,1) and (4,8).
Find the length f the arc of the semicubical $y^2 = x^2$ between the points (1,1) and (4,8). [5]
- Curve: semicubical parabola. The typed equation reads $y^2 = x^2$ but this is a transcription error. The correct semicubical parabola is $y^2 = x^3$. - Endpoints: $(1, 1)$ and $(4, 8)$ Consistency check: For $y^2 = x^3$: at $x=1$, $y^2=1 \Rightarrow y=1$ ✓; at $x=4$, $y^2 = 64 \Rightarrow y=8$ ...