Definite Integrals with Trignometric (?) Equations

[yana]

Hi and thank you for reading this. I'm having problems with understanding the answer to this definite integral:

6 + 5 cos2 θ

cos2 θ

between 0 and pi/4

I distirbute the denom to get

integral [6/ cos^2θ + 5 cos^2θ / cos^2θ ]which simplifies into

6tanθ + 5, since the cos^2theta and cos^2theta would cancel out into 1.

Unfortunately, my ebook tells me the solution is instead 6tan(theta) + 5(theta)

Where does the theta come from attached to the 5? What'd I do wrong?

 

[Deleted member 4993]

Hi and thank you for reading this. I'm having problems with understanding the answer to this definite integral:

6 + 5 cos2 θ

cos2 θ

between 0 and pi/4

I distirbute the denom to get

integral [6/ cos^2θ + 5 cos^2θ / cos^2θ ]which simplifies into

6tanθ + 5, since the cos^2theta and cos^2theta would cancel out into 1.

Unfortunately, my ebook tells me the solution is instead 6tan(theta) + 5(theta)

Where does the theta come from attached to the 5? What'd I do wrong?

\(\displaystyle \int 5 \ d\theta = 5\theta + C\)