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A hint to get started

Subtract a line from a curve or use a triangle

Find the exact area of the region enclosed by y=2+x−x2y=2+x-x^2 and y=x+1y=x+1.

CJC · Lecture · Example 12

The source intersection callout says intersections give the integral limits; a calculator may find them when an exact area is not required. This ask requires an exact answer, so use algebra.

The Teacher note emphasises that a line-and-curve area is a two-curve area, with triangle/trapezium subtraction as an additional option. This guidance is integrated into the two methods.

Read the worked solution