anonymous
  • anonymous
help! definite integral: (2+cos^2theta/cos^2theta)dtheta when dtheta is from pi/4 to 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • 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
anonymous
  • anonymous
oups...cox=cos... typo
amistre64
  • amistre64
\[\int\limits_{0}^{\pi/4} \frac{2+\cos^2(t)}{\cos^2(t)}dt\]

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amistre64
  • amistre64
split it up; like inik states...but with out the typo :)
amistre64
  • amistre64
and we get: [S] 2sec^2(t) + 1 dt
anonymous
  • anonymous
cool! :)
amistre64
  • amistre64
we see that sec^2(t) is the sderivative of tan(t); and 1 is the derivative of t
amistre64
  • amistre64
\[F(t) = 2\tan(t) + t ; [0,\pi/4]\]
amistre64
  • amistre64
tan(0) = 0...so the 0 part is useless.... go with the pi/4
amistre64
  • amistre64
2(1) + pi/4 = 2 + pi/4
amistre64
  • amistre64
11.14159 -------- :) 4
amistre64
  • amistre64
2.785...
anonymous
  • 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
anonymous
  • anonymous
woops *4 to 9
amistre64
  • 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]
amistre64
  • amistre64
2(3) - 9 - [2(2)-4] 6 - 9 - (4-4) = -3
anonymous
  • anonymous
perfect! just had to check

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