A tricky integration problem. Save me

In summary, an integration problem involves finding the area under a curve by summing an infinite number of rectangles. To solve these problems, one must have a strong understanding of calculus and the different integration techniques. Integration problems can be tricky due to their complexity and require practice to improve skills. They have many real-world applications, including calculating distances, volumes, and probabilities in various fields.
  • #1
saksham
16
0
I was asked to integrate( exp(-x) cos(x)) with respect to x with the limits x=0 and x= infinity.
I calculated the indefinite integral to be 0.5 exp(-x) [sin(x)-cos(x)].

I was stuck in the part where we apply limit x approaches infinity of sin(x) and cos x.

Please help me out.


Saksham
 
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  • #2
e^-x goes to zero at infinity, so the other terms arent important, as long as theyre finite, which they clearly are.
 
  • #3
Thanks for your reply StatusX. I really appreciate it.

Saksham
 

FAQ: A tricky integration problem. Save me

What is an integration problem?

An integration problem is a mathematical problem that involves finding the area under a curve by summing an infinite number of rectangles. It is a common problem in calculus and is used to solve a variety of real-world problems.

How do you solve integration problems?

To solve an integration problem, you can use various techniques such as substitution, integration by parts, or trigonometric substitution. It is important to have a solid understanding of calculus and the different integration rules to effectively solve these problems.

What makes an integration problem tricky?

Integration problems can be tricky because they often involve complex functions and require multiple steps to solve. Additionally, the limits of integration and the type of integration rule used can also make a problem more challenging.

How can I improve my skills in solving integration problems?

Practice is key to improving your skills in solving integration problems. Start with simpler problems and gradually work your way up to more complex ones. You can also seek help from a tutor or use online resources to supplement your learning.

What are some real-world applications of integration problems?

Integration problems have various real-world applications, such as calculating the area under a curve to determine the total distance traveled by an object, finding the volume of irregular shapes, and calculating probabilities in statistics. They are also used in fields such as physics, engineering, and economics.

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