Find the continuous function and constant number which satisfies
Evaluate
Evaluate
Evaluate
Evaluate
Evaluate
Evaluate
Prove that
Evaluate
Getting rid of them I'm done! Thanks!
Find the continuous function and constant number which satisfies
Evaluate
Evaluate
Evaluate
Evaluate
Evaluate
Evaluate
Prove that
Evaluate
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.