help! definite integral: (2+cos^2theta/cos^2theta)dtheta when dtheta is from pi/4 to 0

Question

anonymous · Answer

break it to 2 integrals: int(2/cox thera) + int(cox^2(theta))/conx^2)= 2int(1/cox^2) + int(theta) d...
finish it - let me know if there is a problem

anonymous · Answer

oups...cox=cos... typo

amistre64 · Answer

$$\int\limits_{0}^{\pi/4} \frac{2+\cos^2(t)}{\cos^2(t)}dt$$

amistre64 · Answer

split it up; like inik states...but with out the typo :)

amistre64 · Answer

and we get:

[S] 2sec^2(t) + 1 dt

anonymous · Answer

cool! :)

amistre64 · Answer

we see that sec^2(t) is the sderivative of tan(t); and 1 is the derivative of t

amistre64 · Answer

$$F(t) = 2\tan(t) + t ; [0,\pi/4]$$

amistre64 · Answer

tan(0) = 0...so the 0 part is useless.... go with the pi/4

amistre64 · Answer

2(1) + pi/4 = 2 + pi/4

amistre64 · Answer

11.14159
--------   :)
     4

amistre64 · Answer

2.785...

anonymous · Answer

thank you so much this helped a lot i also had a question about the definite integral: ((1-(sqrtx))/sqrtx dx when dx=9 to 4 i got the answer -3 but am not sure on that. if you could help that would be awesome

anonymous · Answer

woops *4 to 9

amistre64 · Answer

this is a plit as well; 

[S] 1/sqrt(x) - 1 dx  ; turn that sqrt into an exponent to deal with it easier..

[S] x^(-1/2) - 1 dx    ; becomes

2sqrt(x) - x ; [4,9]

amistre64 · Answer

2(3) - 9 - [2(2)-4]

6 - 9 - (4-4) = -3

anonymous · Answer

perfect! just had to check