# Calculus Homework #11 due 5-18

Given the graph of $f(x)$ above, calculate the following definite integrals.

1. $\int_{-3}^{-5}f(x)dx$
2. $\int_2^4f(x)dx$
3. $\int_{-3}^3f(x)dx$
4. $\int_3^2f(x)dx$

# Trigonometry Homework #11 due 5-18

Prove each identity.

1. $\cos^4\theta-\sin^4\theta=\cos(2\theta)$
2. $\sin(4x)=4\sin{x}\cos{x}\cos(2x)$
3. $\frac{\sin(2x)}{1+\cos(2x)}=\tan{x}$
4. $\cot\alpha+\tan\alpha=2\csc(2\alpha)$
5. $\tan(\pi-\alpha)=-\tan{\alpha}$