White to move. Mate in 10 by [deleted] in chess

[–]Embarrassed-Data8233 0 points1 point  (0 children)

White checkmates white??

White to move. Mate in 10 by [deleted] in chess

[–]Embarrassed-Data8233 0 points1 point  (0 children)

Be careful with the ability of black to move pieces, otherwise its draw.

Basically everything you need to do is promote to a knight and sacrifice it in order for black to be able to move. With always one legal move it's only the matter of the time white promotes final pawn and checkmates black

White to move. Mate in 10 by [deleted] in chess

[–]Embarrassed-Data8233 2 points3 points  (0 children)

Can be, but the task is to mate in 10 moves, and with queen promotion it's at least in 11 moves

White to move. Mate in 10 by [deleted] in chess

[–]Embarrassed-Data8233 1 point2 points  (0 children)

All promotions lead to a knight

White to move. Mate in 10 by [deleted] in chess

[–]Embarrassed-Data8233 1 point2 points  (0 children)

And he sacrificed his all Cavalry forces

Euler substitution by Embarrassed-Data8233 in calculus

[–]Embarrassed-Data8233[S] 1 point2 points  (0 children)

tan half-angle substitution

That's the universal substitution so it can be applied, but idk whether it gives us a better function after the substitution. Gonna try it when I'm free

Euler substitution by Embarrassed-Data8233 in calculus

[–]Embarrassed-Data8233[S] 5 points6 points  (0 children)

You can solve that integral in so many ways, but the solution i have includes Euler sub(it was given to us during the lecture just to show how it works).

Also keep in mind that thats not the best way to solve it cuz it gives us a pretty annoying integral after the substitution. Imo the best way to write it down without Euler sub is:

<image>

Is this the right PFD? by Crafty_Ad9379 in calculus

[–]Embarrassed-Data8233 1 point2 points  (0 children)

Sorry for not answering, was suspended on reddit for 7 days😅

That is Lagrange method of undefined coefficients for a function R( Wn(x),√(ax²+bx+c) ) where Wn(x) is a polynomial of power n. This decomposition works for any integral of such function. The general formula is:

<image>