(4) F(x) =dt 

2.請評估並在下面表格中寫出每個選項為正確或錯誤的理由。(4 分)

(1) f(x) =

(2) g(x) = log₂(x² + x + 1)

(3) h(x) = sin-1x

(1) dx

(2)(cos3 x + 1)tan x) dx 

(3) ∫2x dx

(4)dx

3. (15%) Suppose that the source of current in an electric circuit is a battery. Then the power output P (in watts) obtained if the circuit has a resistance of R ohms is given by where E is the electromotive force in volts and r is the internal resistance of the battery in ohms. If E and r are constant, find the value of R that will result in the greatest power output. What is the maximum power output?

4. (15%) A solid ball can be obtained by revolving the semi-circular region x² + y² ≤ R², x ≥ 0, about the y-axis. Use the method of disks or cylindrical shells to find the volume of such a solid ball.