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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)