If the area bounded by the curves y = − x 2 + 6 x − 5 , y = − x 2 + 4 x − 3 and the line y = 3 x − 15 is λ 73 , then λ = \_\_\_\_

Question

If the area bounded by the curves y = − x 2 + 6 x − 5 , y = − x 2 + 4 x − 3 and the line y = 3 x − 15 is λ 73 ​ , then λ = \_\_\_\_

TestHub · Accepted Answer

The line meets y = − x 2 + 4 x − 3 at x = 4 and y = − x 2 + 6 x − 5 at x = 5 . The curves meet at x = 1 . Area = ∫ 1 4 ​ [ ( − x 2 + 6 x − 5 ) − ( − x 2 + 4 x − 3 ) ] d x + ∫ 4 5 ​ [ ( − x 2 + 6 x − 5 ) − ( 3 x − 15 ) ] d x = 9 + 6 19 ​ = 6 73 ​ . So λ = 6 .

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