## anonymous 5 years ago help! definite integral: (2+cos^2theta/cos^2theta)dtheta when dtheta is from pi/4 to 0

1. anonymous

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

2. anonymous

oups...cox=cos... typo

3. amistre64

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

4. amistre64

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

5. amistre64

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

6. anonymous

cool! :)

7. amistre64

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

8. amistre64

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

9. amistre64

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

10. amistre64

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

11. amistre64

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

12. amistre64

2.785...

13. anonymous

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

14. anonymous

woops *4 to 9

15. amistre64

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]

16. amistre64

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

17. anonymous