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<h1>✅ Adventure 6 — Activity 1 Solutions</h1>
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<h2>Rectangle Table (Δt = 1)</h2>
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<tr><th>Interval</th><th>Δt</th><th>Velocity</th><th>vΔt</th></tr>
<tr><td>0–1</td><td>1</td><td>0</td><td>0</td></tr>
<tr><td>1–2</td><td>1</td><td>7</td><td>7</td></tr>
<tr><td>2–3</td><td>1</td><td>12</td><td>12</td></tr>
<tr><td>3–4</td><td>1</td><td>15</td><td>15</td></tr>
<tr><td>4–5</td><td>1</td><td>16</td><td>16</td></tr>
<tr><td>5–6</td><td>1</td><td>15</td><td>15</td></tr>
<tr><td>6–7</td><td>1</td><td>12</td><td>12</td></tr>
<tr><td>7–8</td><td>1</td><td>7</td><td>7</td></tr>
<tr><th>Total</th><td></td><td></td><td>84</td></tr>
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<h2>Comparison Table</h2>
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<tr><th>Width (Δt)</th><th>Method</th><th>Sum of Areas</th></tr>
<tr><td>1</td><td>Your Estimate</td><td>84</td></tr>
<tr><td>1/2</td><td>Finer estimate</td><td>85.21</td></tr>
<tr><td>1/4</td><td>Very fine estimate</td><td>85.31</td></tr>
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<h2>3) Integral Calculation</h2>
<p>
S = ∫₀⁸ (8t − t²) dt<br><br>
= [4t² − (1/3)t³]₀⁸<br><br>
= 256 − 512/3<br><br>
= 85⅓ ≈ 85.33 m
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