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# P3 Integration watch

1. (Original post by bodomx)
Integrate sec(x/2)tan(x/2).
I got the answer 2sec(x/2), I think its wrong. anyone who can trace whats wrong?
Nothing, it's right. You can check by differentiating:

y = 2sec(x/2)

t = x/2, y = 2sec t

dy/dx = dy/dt.dt/dx

dy/dx = 2sec t.tan t.1/2

dy/dx = sec(x/2)tan(x/2)
2. OK. Here's another one.

(e^x-e^-2)^2
3. (Original post by bodomx)
OK. Here's another one.

(e^x-e^-2)^2
There's nothing wrong with that either. Expand the bracket: (e^2x - 2e^x.e^-2 + e^-4) and integrate:

∫(e^2x - 2e^x.e^-2 + e^-4) dx = ∫ e^2x dx - 2e^-2∫e^x dx + ∫e^-4 dx

= (1/2)e^2x - 2e^-2.e^x + xe^-4 + C
4. how do u integrate INT(e^sinx.cosx) dx??? using substitution u=sinx
5. (Original post by lgs98jonee)
how do u integrate INT(e^sinx.cosx) dx??? using substitution u=sinx
Assuming its (e^sinx)cosx, then u=sin x, gives
INT e^u du = e^u + C = e^sinx + C
6. that easy eh

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