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Q.

The following figure shows the graph of continuous function y=f(x) on the interval  [1,3]. The points A,B,C have coordinates (1,1), (3,2), (2,3) respectively, and the lines  l1 and  l2 are parallel, with  l1 being tangent to the curve at C. If the area under the graph of  y=f(x) from  x=1  to x=3  is 4 square units, then the area of the shaded region(in square units) is:

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answer is 2.

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Detailed Solution

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13f(x)dx=4

Shaded area = Trapezium Area – Area under curve 

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=(52+72)(31)24=2

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The following figure shows the graph of continuous function y=f(x) on the interval  [1,3]. The points A,B,C have coordinates (1,1), (3,2), (2,3) respectively, and the lines  l1 and  l2 are parallel, with  l1 being tangent to the curve at C. If the area under the graph of  y=f(x) from  x=1  to x=3  is 4 square units, then the area of the shaded region(in square units) is: