Trig Questions (1 Viewer)

rand_althor · May 26, 2015

Hey, I didn't manage to get the right answer for these questions:

Could someone please help?
Thanks!

kawaiipotato · May 26, 2015

For 1, draw up the two graphs, and integrate with borders making sure to put absolute values wherever, the area goes under the x-axis.
For 2, note that :
$\frac{d}{dx} (-cotx) = (cscx)^{2}$
So by integrating both sides
$\int \frac{d}{dx} (-cotx) = \int (cscx)^{2} dx$
$-cotx + C= \int (cscx)^2 dx$
This should be on the list of standard integrals so you can just quote
$\int (cscx)^2 = -cotx + C$
For 3, use the identity $(cscx)^2 - (cotx)^2 = 1$
$(cotx)^2 = (cscx)^2 - 1$
$\int (cotx)^2dx = \int (cscx)^2 - 1 dx$
$\int (cotx)^2 dx= -cotx - x + C$

rand_althor · May 26, 2015

Thank you!

Trig Questions (1 Viewer)

rand_althor

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kawaiipotato

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rand_althor

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