Integration. I'll always find my way back to Calculus. ๐ I came across this problem on an exam review sheet. There was a note on the sheet for the students to skip this problem because, it wouldn't appear on the exam. I was intrigued so, it's appearing on the blog this week. ๐ฉ๐ฟ๐ซ I don't really recall solving an integral like this when I first learned integration in college. Since that was too long ago, my recollection is probably off.
To solve this week's problem in completion, you need to recall the following math skills:
✔️ How to perform a substitution technique
✔️ How to perform completing the square method
(Do you see ๐ the hint I gave above? You're welcome. ☺️) Here is WMP! #46:
Check back on Friday, April 16th for the solution, which will be posted below ⬇️.
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✏️๐ Solution Time! ๐✏️
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Here is my solution. I hope you can follow it. My goal is for it to be clear. I got started by dealing with the denominator.
Next, I rewrote the original problem with the completed square and saw that I can now perform u-substitution to simplify the integrand.
After completing the u-substitution, I wasn't able to integrate the function. Upon inspection, (hopefully) it can be seen that trigonometric substitution needs to be used to complete the integration.
Ahhh...integration is complete...but the process isn't complete. ๐คจ Conversions need to occur so that the answer can in term of x to match the original problem. Plus, I need to figure out what cos ๐ is equal to.
Now, the process is complete! ๐ฅณ Let me know what you did differently, or if you didn't do anything differently.
▪️ Leave your responses down below and let me know what you thought about this week's problem.
Thanks for solving with me this week!
Up next, WMP! #47. ๐ช๐ฟ
Cheers!
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