Find the continuous function and constant number which satisfies
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Prove that
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Getting rid of them I'm done! Thanks!
Good, old-fashioned parts is one way to go on this one. Though, you'll have to apply it several times.Evaluate
Let
Do the parts thing again:
Continue in this fashion and you should have a on the right side. Add it to both sides and divide by 2 and you should end up with:
I wanted to show my method of doing this integral. It's been bugging me. No, I am not vying for Best Integrator. I am sure Big K has that in the bag. I, like K, just enjoy doing these integrals. They are like little puzzles to figure out. I see why Plato says it is rather pointless, but why not just for fun and not practicality?.
First, I use the identity:
Now, make the sub , and we get:
Now, use the identity
and .
We get:
So, we get:
Solve for I and get:
Of course, the negative at the beginning results in a positive solution.