Integration (1 Viewer)

[untouchablecuz]

/√(16-x²)
|----------- dx
/ x²

Find using the substitution x=4sinθ

I get up to:

/cos²θ
|-------dθ
/sin²θ

But now i'm stuck (assuming i'm correct).

 

[lolokay]

from there you would just go

= | cot²θ.dθ
= | (csc²θ-1).dθ
= -cotθ - θ + C
= -[√16-x²]/x - sin^-1[x/4] + C

 

[untouchablecuz]

from there you would just go

= | cot²θ.dθ
= | (csc²θ-1).dθ
= -cotθ - θ + C
= -[√16-x²]/x - sin^-1[x/4] + C

How do you integrate cosec²θ? I've never come across it. Thanks.

 

[clintmyster]

How do you integrate cosec²θ? I've never come across it. Thanks.

it doesnt appear on the standard integrals table so I guess its one of them you need to know

 

[lolokay]

you could do it like

cosec²θ = sec²[pi/2-θ]

| sec²[pi/2-θ] .dθ
= -tan[pi/2-θ]
= -cotθ

 

[untouchablecuz]

That makes sense. Thanks