Class 12 Applications Of Integrals · Very Long Answer5 Marksarea_by_integration
Class 12 Maths · Applications Of Integrals · Very Long Answer #31
Using integration, find the area of the triangular region with sides y=2x+1,y=3x+1,x=4.
✅ Step-by-Step Solution
Final Answer: \(8\) square units
- The sloping sides meet at (0,1); at x=4 their endpoints are (4,9),(4,13). The upper line is 3x+1 and lower line is 2x+1.
- Use upper minus lower strip widths: \(x\) for x∈\(\left[0, 4\right]\).
- Hence A=\(\int_{0}^{4}(x)\,dx\).
- Primitive \(\frac{x^{2}}{2}\), endpoint difference \(8\).
- Therefore the area is \(8\) square units.
📋 CBSE Stepwise Marking Scheme
- [1 mark] The sloping sides meet at (0,1); at x=4 their endpoints are (4,9),(4,13). The upper line is 3x+1 and lower line is 2x+1.
- [1 mark] Use upper minus lower strip widths: \(x\) for x∈\(\left[0, 4\right]\).
- [1 mark] Hence A=\(\int_{0}^{4}(x)\,dx\).
- [1 mark] Primitive \(\frac{x^{2}}{2}\), endpoint difference \(8\).
- [1 mark] Therefore the area is \(8\) square units.
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