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
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
