1. Evaluate the integral $\int_0^1 \frac{-7y}{e^{2y}} dy$
2. Evaluate the indefinite integral $\int \cos^6 x \tan^3 x \, dx$
3. Evaluate the integral $\int_0^2 -10x^3 \sqrt{x^2 + 4} \, dx$. In your write-up, explain the three trig substitutions possible
for different radicands, based on the right triangle, indicating which is correct in this case and why. A full
write-up would indicate the circumstances to use each of the other two.
4. Let $f(x)$ be a function that is defined and has a continuous derivative on the interval $(2, \infty)$. Assume also
that $f(4) = -14$, that $|f(x)| < x^4 + 10$, and that $\int_4^\infty f(x)e^{-x/3} dx = 2$. Determine the value of
$\int_4^\infty f'(x)e^{-x/3} dx$.
