Weekly Math Problem! #21

Integration. So, here we are again with another integration problem. If you've done last week's problem, then you've already done some of the work needed to do this week's problem. 🤓 Wait, you haven't seen last week's problem?! Pause....check out WMP! #20. 

Last week I mentioned that partial fraction decomposition is an important technique that allows you to "simplify" some complicated rational expressions by breaking them down into smaller parts. WMP! #21 is such a problem that requires the technique of partial fraction decomposition.

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️ How to integrate rational expressions

        ✔️ Partial fraction decomposition

WMP! #21 wants us to...

Happy solving!

Check back on Friday, September 25th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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Again, if you take a look at WMP! #20, you will see that it has the same rational expression as this week's problem. So, when you're given a rational expression, similar to that one, to integrate, you can see what needs to be done to carry out the integration. Here's how I carried it out:

That's all I've got! (I actually really like this problem.)  

 

▪️ How did you feel about this week's problem?? 

▪️ Did you carry out the integration differently than I did??

▪️ Comment below with your responses and let me know what you thought about this week's problem.

See you right back here next week for WMP! #22, the last problem of September.

🤓

Cheers!

The Younge Lady

Weekly Math Problem! #20

Partial Fractions Decomposition. This topic is one I didn't hear much about until I was required to integrate certain types of rational expressions. It's an important technique that allows you to "simplify" some complicated rational expressions by breaking them down into smaller parts, so that you may more easily compute problems that involve them. This week's problem comes from the Pure Mathematics, CAPE (Caribbean Advanced Proficiency Examination) materials.

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️  How to use partial fraction decomposition

        ✔️  Simplifying rational equations

        ✔️  Working with undetermined coefficients

    

WMP! #20 says...

Happy solving! 

Check back on Friday, September 18th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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...And we're back to decompose this fraction into the components that were combined to get it in the first place. Here are the steps I took to do so:

There you have it!  

 

▪️ Were you able to decompose the fraction?? 

▪️ Comment below with your responses and let me know what you thought about this week's problem.

See you right back here next week for WMP! #21

(Now let's see if you can guess what next week's problem is going to be.)

🤓

Cheers!

The Younge Lady

Weekly Math Problem! #5

Improper Integrals. A calculus thing. There's just something about solving integrals that I find very intriguing and that's probably because it requires more thought and "tricks" to get the solution, as compared to taking derivatives. But that's also the annoying thing--sometimes trying to figure out what sort of "tricks" are needed to help you figure the integral out. 🙄 

Like verifying trigonometric identities (see WMP! #3), these type of problems are also like puzzles to me. To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Methods for solving integrals

    ✔️  Finding limits 

    ✔️  Using logarithmic rules 

It's been a super long while since I've solved an improper integral so...here goes WMP! #5... 

Happy solving! Check back on Friday, June 5th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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I don't know how much calculus you remember. I don't know how many limit rules you remember. I don't how much you remember about exponential functions. But, if you're like me, you didn't remember enough right off the top of your head to get this problem done quickly. 🤷🏿‍♀️ 🥴 

◾️ Was your solution this long?? (...Or is it just me??) 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

Coming up next...WMP! #6 👀

Cheers!

The Younge Lady