1. Find the average of the function f(x) = x sin x between x =0 and x=π.

2. The eror functon erf(x) is defined as erf(x)=. Use this formula to find the integral .

3.For dx dy ,(1)sketch the region of integration； (2) switch the order of integration and evaluate the integral.

4. Evaluate the line integral ，where C. line segment from (1, 1) to (Hint:)

5.Find the area of the region Iying between the inner and outer loops of the limacon r(θ) =1-2sinθ.

(a) CISC

(b) RISC

(e) Reconfigurable Computing

(d) Multi-core Processor

[Problem 2] Suppose we are considering a change to an instruction set. The base machine is a load-store machine. Measurements of the load-store machine showing the instruction mix and clock cycle counts per instructions are given in the following table:       Let's assume that 25% of the ALU operations directly use a loaded operand that is not used again. We propose adding ALU instructions that have one source operand in memory. These new register-memory instructions have a clock cycle count of 2. Suppose that the extended instruction set increases the clock cycle count for branches by 1, but it does not affect the clock eycle time, Would this change improve CPU performance? Explain your answer. (20%)

[Problem 3] A set associative cache has a block size of four 64-bit words and a set size of 4. The cache can accommodate a total of 256K words. The main memory size that is cacheable is 512M * 64 bits. Design the cache structure and show how the processor's addresses are interpreted. (20%)

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