Further integration — Question 213
Original QCE Vault practice · 5 marks
Q213 · Practice questionTechnology-freeComplex unfamiliar5 marks
QUESTION 213 (5 marks)
The curves y=6−0.5x2 and y=x+2 enclose a finite region. 
a)Find the intersection points exactly.
b)Find the exact area of the enclosed region.
WORKED SOLUTION
Practice marking scheme
5 marksANSWERArea=∫−42[(6−0.5x2)−(x+2)]dx=Integral(4−x−0.5x2)dx=[4x−2x2−6x3]−42=18 square units. Worked solution
Part (a): Solve 6−0.5x2=x+2→x2+2x−8=0→x=−4,2. Corresponding points are (−4,−2) and (2,4). Part (b): Area=∫−42[(6−0.5x2)−(x+2)]dx=Integral(4−x−0.5x2)dx=[4x−2x2−6x3]−42=18 square units. Part (a): completes the requested reasoning and obtains a correct result.
Part (b): completes the requested reasoning and obtains a correct result.
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