GATE CE 2022 Set 1 — Question 2
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Engineering Mathematics → Calculus → Area & Volume via Integration
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Question
Two straight lines pass through the origin . One of them passes through the point and the other passes through the point . What is the area enclosed between the straight lines in the interval on the -axis?
Correct answer
(A) 0.5
Solution
1.Find the equations of the two lines:
- Line 1 passes through and . Its slope . Equation: .
- Line 2 passes through and . Its slope . Equation: .
3.Evaluate the integral:
Alternatively, the area is a triangle with vertices , , and .Base length (along ) .
Height (perpendicular distance from origin to ) .
Area .
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