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A hint to get started

Distinguish a logarithm from its absolute-value graph

(i) Find ∫ln⁡(2x−1) dx\int\ln(2x-1)\,dx.

(ii) Sketch y=∣ln⁡(2x−1)∣y=|\ln(2x-1)|, stating asymptotes and axis intercepts.

(iii) Find the exact area bounded by y=∣ln⁡(2x−1)∣y=|\ln(2x-1)|, the x-axis, x=3/4x=3/4 and x=3/2x=3/2.

(iv) Find the volume when the region bounded by y=ln⁡(2x−1)y=\ln(2x-1), the x-axis, x=3/2x=3/2 and x=3x=3 rotates completely about the y-axis.

[2015/HCI/II/4]

CJC · Review problems · Question 13

The integration question uses ln, while the sketch and area use its absolute value.

Read the worked solution