CBSE Class 12 Mathematics 2026 Main Paper 65/3/3 · Q364 Marksarea_under_lines
CBSE Class 12 Mathematics 2026 Main Paper 65/3/3 · Question 36 (Applications Of Integrals)
A triangular park has vertices A=(0,4), B=(−2,0) and C=(3,0). O is the origin. Segment AO divides the park into OAC, where running sports are allowed, and AOB, where they are restricted.
Part (1) 1 Marks
Find the boundary line AB.
Answer: 2x−y+4=0.
- The slope from B to A is (4−0)/(0−(−2))=2.
- Since A is on the y-axis, y=2x+4.
Part (2) 1 Marks
Find the boundary line AC.
Answer: 4x+3y=12.
- The slope from A to C is (0−4)/(3−0)=−4/3.
- The line is y=4−4x/3, equivalently 4x+3y=12.
Part (3) 2 Marks
Use integration to find the area of OAC.
Answer: 6 square units.
- The upper boundary on 0≤x≤3 is y=4−4x/3.
- Integrate from 0 to 3 to obtain [4x−2x²/3]₀³.
- The area is 6 square units.
Part (4) 2 Marks
Use integration to find the area of AOB.
Answer: 4 square units.
- The upper boundary on −2≤x≤0 is y=2x+4.
- Integrate to obtain [x²+4x] from −2 to 0.
- The area is 4 square units.