Help Solving Integral Limit: x to 1

erogol · 2009-03-27T22:26:08+00:00

lim x \int cost / t^2 (integral x to 1) x goes infitine

Thread starter erogol
Start date Mar 27, 2009
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Limit

In summary, an integral limit is a mathematical concept used to represent the value that a function approaches as the independent variable approaches a specific value. To solve for an integral limit, you must determine the function and the value it is approaching, and then use techniques such as substitution, integration by parts, or partial fractions. Solving for an integral limit is important in various fields and can help in understanding the behavior and making predictions about a function. Some common techniques for solving an integral limit include the fundamental theorem of calculus, u-substitution, integration by parts, and partial fractions. While a calculator can be used to approximate the value of the limit, it is recommended to check the work by hand for accuracy.

Mar 27, 2009

erogol

lim x [tex]\int cost / t^2[/tex] (integral x to 1) x goes infitine

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Mar 28, 2009

CompuChip

Science Advisor

Homework Helper

Did you mean:
[tex]\lim_{x \to \infty} \int_x^1 \frac{\cos t}{t^2} \, dt[/tex]
?

Mar 28, 2009

erogol

yes:) but there is a x before the integral

Mar 28, 2009

MathematicalPhysicist

Gold Member

Hint: t is in [x,1] i.e 1/t^2 is in [1,1/x^2].

Mar 28, 2009

intrepid_nerd

integrate via parts and keep track of your signs

1. What is an integral limit?

An integral limit is a mathematical concept that represents the numerical value that a function approaches as the independent variable (usually denoted as x) approaches a specific value. It is often used to evaluate the area under a curve or the total accumulation of a quantity over a given interval.

2. How do I solve an integral limit?

To solve an integral limit, you must first determine the function and the value that the independent variable is approaching. Then, you can use techniques such as substitution, integration by parts, or partial fractions to evaluate the integral and determine the limit.

3. Why is it important to solve for an integral limit?

Solving for an integral limit can help you calculate important quantities in fields like physics, engineering, and economics. It can also help you understand the behavior of a function and make predictions about its values in specific scenarios.

4. What are some common techniques for solving an integral limit?

Some commonly used techniques for solving an integral limit include the fundamental theorem of calculus, u-substitution, integration by parts, and partial fractions. Choosing the most appropriate technique depends on the form of the integral and the given limits.

5. Can I use a calculator to solve for an integral limit?

Yes, you can use a calculator to solve for an integral limit. However, it is important to remember that calculators can only approximate the value of the limit and may not provide an exact answer. It is always recommended to check your work by hand to ensure accuracy.