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Math 9B
Due date: 11:59 pm of the discussion day Consider f(x) = 3x− 1 and g(x) = x2 − 4. 1. (2 points) Compute ∫ 2 −2 f(x) dx as a signed area on the plane. 2. (2 points) If moreover ∫ 2 3 f(x) dx = −13 2 , compute ∫ 3 −2 (2f(x) + 4) dx. (Hint: first find∫ 3 −2 f(x) dx using (1)) 3. (2 points) Compute the right-endpoint Riemann approximation of ∫ 2 −1 f(x) dx, using a partition of 3 subintervals. Include the graph and rectangles in your solution. 4. (2 points) Compute the midpoint Riemann approximation of ∫ 3 −1 g(x) dx, using a partition of 2 subintervals. Include the graph and rectangles in your solution. 5. (2 points) Compute ∫ 2 0 g(x) dx using the definition of the Riemann integral. (Hint: n∑ k=1 k2 = n(n+ 1)(2n+ 1)