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Applications of Integrals Calculator

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Example
Created on 2024-06-20Asked by Daniel Sanchez (Solvelet student)
Find the area under the curve y=x2 y = x^2 from x=0 x = 0 to x=2 x = 2 .

Solution

Step 1: Identify the function and the limits of integration. The function is y=x2 y = x^2 and the limits are x=0 x = 0 to x=2 x = 2 . Step 2: Set up the integral to find the area under the curve: ∫02x2 dx. \int_{0}^{2} x^2 \, dx. Step 3: Evaluate the integral: ∫x2 dx=x33+C. \int x^2 \, dx = \frac{x^3}{3} + C. Step 4: Apply the limits of integration: x33∣02=233−033=83. \left. \frac{x^3}{3} \right|_{0}^{2} = \frac{2^3}{3} - \frac{0^3}{3} = \frac{8}{3}. Step 5: Conclusion. The area under the curve y=x2 y = x^2 from x=0 x = 0 to x=2 x = 2 is 83 \frac{8}{3} . Solved on Solvelet with Basic AI Model
Some of the related questions asked by Mason Nguyen on Solvelet
1. Determine the enclosed area by the curve y=x2 y = x^2 and the x-axis over the interval [0,2] [0, 2] 2. Calculate the volume of the bounded solid generated by revolving the region by y=x2 y = x^2 and the y y -axis about the y y -axis using the disk method.,
DefinitionIntegrals are mathematical tools to evaluate those quantities like area, volume, mass and other quantity which is related to physical property. They are used to find the area between curves, to find the volume of solids of revolution, to find the center of mass, to find the work done by a force, to find probabilities in statistics, and many, many more applications. Integrals are found in many scientific fields all-around, like physics, engineering, and so on. In physics, for example, one would integrate the power function to get the total energy stored in a system with respect to time.
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