# Help with Integrating and Finding Concavity of a Curve

• jhayes25
In summary, the conversation revolved around finding the definite integral of (1/(1+t^2))dt from 0 to x^2 and determining the interval for which the curve is concave upward. It was suggested to use a trigonometric substitution or to recognize that the integrand is the derivative of arctan.
jhayes25

## Homework Statement

Not real good with the easy text stuff yet so ill give it a shot.

definite integral of (1/(1+t^2))dt from 0 to x^2
then find the interval for which the curve is concave upward.

I totally forgot how to integrate problems like this. It is some sort of substitution I know.

Help?

Would the integral of this involve a natural log?

Last edited:
What you have in your integral is arctan. Probably something you should memorize.

You'd need a trigonometric substitution for that integral. It works out quite neatly in the end.

Or recognise that the integrand is the derivative of arctan.

Last edited:

## What is the definition of integration?

Integration is a mathematical process of finding the area under a curve. It involves breaking down a shape into smaller, simpler shapes and adding up their areas to find the total area.

## How do I find the concavity of a curve?

To find the concavity of a curve, you need to take the second derivative of the function and then analyze its sign. If the second derivative is positive, the curve is concave up. If it is negative, the curve is concave down. If it is zero, the curve has a point of inflection.

## What is the purpose of integrating a curve?

The purpose of integrating a curve is to find the area under the curve, which can be used in various real-world applications such as calculating volumes, distances, and probabilities.

## What are the different methods of integration?

There are several methods of integration, including the power rule, substitution, integration by parts, and trigonometric substitution. Each method is used for different types of functions and can be helpful in solving complex integration problems.

## What is the difference between definite and indefinite integration?

Definite integration involves finding the exact value of the area under a curve between two specific points. Indefinite integration, on the other hand, involves finding a general solution for the integral without specifying the limits of integration.

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