Use define integrals to calculate the area under the graph of y=tanx between x=a to x=b. (hint: write tangent in the form of sinx/cosx)

Question

How would you do this?

Answer 1

area=int (sinx/cosx)dx
let Y=cosx
dY=-sinx dx
area=int( -dY/Y )dY= -ln Y overlimits=-ln(abs(cosb))+ln(abs(cosa))
check my thinking. abs= absolutevalue

Answer 2

so you're saying:

-ln |cosb| + ln |cosa|

I'm still a little confused. Can you help clarify?

int (sinx/cosx)dx
int( -dY/cosx )dY
-ln cosx overlimits
= -ln |cosb| + ln |cosa|

Answer 3

I doubt if I can make it plainer than that, every step is shown. The absolute values is because the log of a negative number is not defined, if that is your question.

Answer 4

Ok. I got it now. Thank you!