# Definite Trig Integrals: Changing Limits of Integration

$$\int_0^{\pi/4} \sec^4 \theta \tan^4 \theta\; d\theta$$

I used the substitution: let $u = \tan \theta$ ... then $du = \sec^2 \theta \; d\theta$.

I know that now I have to change the limits of integration, but am stuck as to how I should proceed.

Should I sub the original limits into $\tan \theta$ or should I let $\tan \theta$ equal the original limits and then get the new limits?

And if it help, the answers of the definite integral is supposed to be $0$.

$\sec^4\theta = (1 + \tan^2\theta)\cdot \sec^2\theta$, then substitute $u = \tan\theta$ to get:
$$I = \displaystyle \int_{0}^1 (u^6 + u^4) du = \left.\dfrac{u^7}{7} + \dfrac{u^5}{5}\right|_{0}^1 = \dfrac{12}{35}.$$