Integration question (obtained from arc length question)

MHB
Thread starter annie122
Start date Feb 5, 2014
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Arc Arc length Integration Length

In summary, integration is a mathematical process used to find the area under a curve by summing up infinitesimally small rectangles. It has various real-life applications in fields such as physics, engineering, economics, and statistics. There are two types of integration: definite and indefinite, with definite integration providing the exact value of the area within a specific range, and indefinite integration providing a general antiderivative without specifying a range. Integration is an essential concept in calculus as it allows for the calculation of areas, volumes, and surface areas of three-dimensional objects, making it crucial for solving real-world problems. To solve an integration question, one must follow the fundamental rules of integration, have a good understanding of integral properties, and practice solving various types

Feb 5, 2014

annie122

how do i integrate the function

sqrt(1 + 1/2(y^1/2 - y^(-1/2))^2) from 0 to 1??

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Feb 5, 2014

MarkFL

Gold Member

MHB

Can you post the original problem in its entirety so we can ensure you have obtained the correct integrand?

1. What is integration?

Integration is a mathematical process that involves finding the area under a curve by summing up infinitesimally small rectangles.

2. How is integration used in real life?

Integration is used in various fields such as physics, engineering, economics, and statistics to solve problems involving quantities that change continuously over time or space.

3. What is the difference between definite and indefinite integration?

Definite integration involves finding the exact value of the area under a curve within a specific range, while indefinite integration involves finding a general antiderivative of a function without specifying a range.

4. Why is integration important in calculus?

Integration is an essential concept in calculus as it allows us to calculate the area under a curve, which is crucial in solving various real-world problems. It is also used to find the volume and surface area of three-dimensional objects.

5. How do I solve an integration question?

To solve an integration question, you need to follow the fundamental rules of integration, such as the power rule, substitution rule, and integration by parts. You also need to have a good understanding of the properties of integrals and practice solving various types of integration problems.