The last part of a integral

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In summary, the last part of an integral is the result, or definite integral, representing the area under a curve between two points on a graph. It is calculated by determining the upper and lower limits of integration and evaluating the function at these points. The last part of an integral is important in mathematics because it has numerous applications and allows for solving complex equations. Common techniques for evaluating it include substitution and integration by parts, but there are limitations such as only being applicable to continuous functions and requiring a strong understanding of calculus.
  • #1

ddr

8
0

Homework Statement



4
∫ √x/(1+√x)
0

Homework Equations





The Attempt at a Solution



t=√x ; x=t^2 ; dx= 2t

2
∫ (2t^2)/(1+t)
0

and now?
thanx
 
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  • #2
Simplify your denominator with another substitution.
 
  • #3
Bring the 2 outside the integral and then add and subtract 1 in the numerator.
 
  • #4
First subtract and then add 1 in the numerator.

Daniel.
 
  • #5
Hi ddr,

Perform polynomial algebraic division and integrate the result directly.
 

What is the last part of an integral?

The last part of an integral is the result, also known as the definite integral, which represents the area under a curve between two points on a graph. It is typically denoted by the symbol ∫ and is often used in calculus and other branches of mathematics.

How is the last part of an integral calculated?

To calculate the last part of an integral, one must first determine the upper and lower limits of integration, which represent the two points on the graph between which the area is being calculated. Then, the function being integrated must be evaluated at these limits and the difference between the two values is taken as the result.

Why is the last part of an integral important in mathematics?

The last part of an integral is important because it allows us to find the exact area under a curve, which has numerous applications in mathematics, physics, and other fields. It also allows us to solve differential equations and evaluate complex functions that cannot be easily solved using other methods.

What are some common techniques for evaluating the last part of an integral?

There are several techniques for evaluating the last part of an integral, including substitution, integration by parts, and using trigonometric identities. These techniques can be used to simplify the integral and make it easier to calculate the result.

Are there any limitations to using the last part of an integral?

Yes, there are some limitations to using the last part of an integral. For example, it can only be used for continuous functions and may not always give an exact result for more complex functions. It also requires a good understanding of calculus and mathematical concepts to accurately evaluate the integral.

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