Evaluating Area of Triangle using Integration

Here is a Multi choice question to Evaluate Area of Triangle by Integration. You can find similar set of questions at TutorVista Blogs.

Topic : Area of Triangle by Integration

Below example will help you to identify correct choice and get reasons for, why remaining choices are incorrect.

Question : use the graph of Integrand and area to evaluate the integral ₂∫⁴ (x/2 + 3) dx

a) 21
b) 29
c) 17
d) 46

Solution :
Choice (a) is correct.
y = x/2 + 3 is a straight line above x-axis for x ≥ -6














₂∫⁴ (x/2 + 3) dx = = area of quadrilateral DBCE= area of the triangle ACE – area of the triangle ABD

= 1/2 * 5 * 10 - 1/2 * 2 * 4 = 25 - 4 = 21

choice b is incorrect because of the error in adding the areas of the triangles ACE and ABD instead of subtracting.

Choice c is incorrect because of the error in missing to divide 8 by 2 in the area of the triangle ABD.

Choice d is incorrect because of the error in missing to divide 50 by 2 in the area of the triangle ACE.

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