Instructions: Complete the homework in the space below. Use proper mathematical notation. When solving problems, use the format discussed in the class. If work is not in the correct format and/or is not easy to read, it will get zero points. Note: The following directions are important, or points will be taken off even if the answer looks right. Write integrals in proper notation. For example, if the following derivative is specified, /,(x)=4x4 sin x dx then find the function f(x) by writing the integral and solving it, making sure to include the dx (or dt, or similar term) in the integral, f(x)-I x2+ sin x dr=-x3-cosx+ C Note f(x)-is required, not just the integral. Given a value such as f (0)=1 , use it to evaluate the constant: C=2 f(x)=1x3-cos x +2 Antiderivatives 1. a. Let f" (x) = 20x1+ 16x + 32. Use indefinite integration to find f(x). b. Use the initial condition f(0)- 12 to evaluate the constant. Then rewrite the entire function with the new value for the constant.