Integrate sinx

[Chikis]

Integrate sinx

[Chikis]

If y^2 - x^2 = 5(y-x)^2, find x:y

[Math Tutor]

Divide by y-x the both sides

[leesajohnson]

If y = sinx then dy/dx = cosx

So ∫ cosx dx = sinx + C

[Guest]

Chikis wrote "If y^2 - x^2 = 5(y-x)^2, find x:y"
First if x= y then y- x and y^2- x^2 are 0 so any value of x= y is a solution.

If y is not equal to 0 then we can divide by y- x to get y+ x= 5, y= 5- x.

All pairs (x, x) and (x, 5- x) satisfy the equation and any solution is one of those two forms.

(What does this have to do with "integrate sinx"?)

[HallsofIvy]

If y = sinx then dy/dx = cosx

So ∫ cosx dx = sinx + C

But the question asked was the integral of sin x, not cos x.

For that we need "if y= cos(x) then dy/dx= -sin x, so that if y= -cos x then dy/dx= -(-sin x)= sin x.

So ∫ sin x dx= -cos x+ C,"