- #1
DottZakapa
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- TL;DR Summary
- double integral
could please some one explain the inequality on the right?
in particular how should i see
and
thanks
Look at the graphs of ##y = x## and ##y = x^2## on the interval [0, 2]. When ##x \in [0, 1]##, which graph is higher? Same question when ##x \in [1, 2]##.DottZakapa said:why?
A double integral is a type of mathematical operation used to calculate the volume of a three-dimensional object. It involves integrating a function over a two-dimensional region.
A single integral involves integrating a function over a one-dimensional interval, while a double integral involves integrating a function over a two-dimensional region. This allows for the calculation of volume rather than just area.
The purpose of using a double integral is to calculate the volume of a three-dimensional object or the area of a two-dimensional region. It is a useful tool in many fields of science and engineering, such as physics, economics, and fluid mechanics.
Evaluating a double integral involves breaking down the two-dimensional region into smaller, simpler shapes such as rectangles or triangles. Then, the integral is calculated for each of these shapes and added together to get the final result.
Double integrals have many real-life applications, such as calculating the volume of a solid object, finding the center of mass of an irregular shape, and determining the probability of an event in statistics. They are also used in fields such as engineering, economics, and physics to solve various problems and make predictions.