Use Fundamental Theorem of Calculus to find the shaded area R. Note: Area is always positive. You will get negative number for your integral which means area is under the x-axis. So integral gets negative but we always write area as a positive number
Use Fundamental Theorem of Calculus to find the shaded area R. Note: Area is always positive. You will get negative number for your integral which means area is under the x-axis. So integral gets negative but we always write area as a positive number
Use Fundamental Theorem of Calculus to find the shaded area R. Note: Area is always positive. You will get negative number for your integral which means area is under the x-axis. So integral gets negative but we always write area as a positive number
Transcribed Image Text:The image presents a graph of the function \( y = \frac{x^2}{3} - 4 \).
**Description:**
- **Axes:** The graph is plotted with the x-axis and y-axis intersecting at the origin (0,0).
- **Function Plot:** The curve represents the function \( y = \frac{x^2}{3} - 4 \), and it is a downward-opening parabola due to the quadratic term \(\frac{x^2}{3}\).
- **Shaded Region (R):** The area shaded in blue beneath the curve and above the line \(y = -3\). The curve crosses the y-axis at \(-4\) and the x-axis at the points \((-2, 0)\) and \((2, 0)\).
- **Points of Intersection:** The parabolic curve passes through the x-axis at points (-2, 0) and (2, 0).
This visualization can help in understanding quadratic functions and the areas they cover above the x-axis or below the x-axis.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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