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Split three horizontal area pieces

Find the area of the region bounded by 1−x=(y+1)21-x=(y+1)^2, the y-axis, and the lines y=−3y=-3 and y=2y=2.

CJC · Lecture · Example 11

Both copies already contain the three shaded pieces, labelled x/y bounds, rearrangement callout, complete signed-integral setup and 9⅓ final answer. These were compared rather than attributed as Teacher-only additions.

Use the y-axis crossings to split the interval before evaluating. The explicit antiderivative and intermediate numerical contributions here are independently authored.

Read the worked solution