GATE CS 2015 Set 2 — Question 56
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Engineering Mathematics → Calculus → Integration
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Question
Let and denote the area of the region bounded by and the X-axis, when varies from to . Which of the following statements is/are TRUE?I) is continuous in
II) is not bounded in
III) is nonzero and finite
II) is not bounded in
III) is nonzero and finite
Correct answer
(C) II and III only
Solution
Analyze the function on .I) Continuity: At , the denominator is 0, so is undefined. Thus, is discontinuous at . Statement I is FALSE.II) Boundedness: . The function is unbounded. Statement II is TRUE.III) Area : The area is given by the integral of the absolute value of the function:Due to symmetry is an even function:The area is 3, which is nonzero and finite. Statement III is TRUE.Since II and III are true, option (C) is correct.
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