Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Problem:** Find the area of the region bounded above by \( y = -x^2 + 5 \) and below by \( y = 1 \). **Graph Description:** The graph shows a parabola represented by the equation \( y = -x^2 + 5 \) with its vertex at the point (0, 5). The parabola opens downwards, intersecting the x-axis at points (-√5, 0) and (√5, 0). A horizontal line is drawn at \( y = 1 \). The shaded region between the parabola and the horizontal line represents the area that needs to be calculated. **Choices:** - **a.** \( \frac{8}{3} \) - **b.** \( \frac{16}{3} \) - **c.** \( \frac{32}{3} \) (correct answer, selected) - **d.** 36
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Transcribed Image Text:**Problem:** Find the area of the region bounded above by \( y = -x^2 + 5 \) and below by \( y = 1 \). **Graph Description:** The graph shows a parabola represented by the equation \( y = -x^2 + 5 \) with its vertex at the point (0, 5). The parabola opens downwards, intersecting the x-axis at points (-√5, 0) and (√5, 0). A horizontal line is drawn at \( y = 1 \). The shaded region between the parabola and the horizontal line represents the area that needs to be calculated. **Choices:** - **a.** \( \frac{8}{3} \) - **b.** \( \frac{16}{3} \) - **c.** \( \frac{32}{3} \) (correct answer, selected) - **d.** 36
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Step 1: We have to find area
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Step 2: Finding the point of intersection
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Step 3: Calculating area
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