The area of the region bounded by the lines y = mx, x = 1, x = 2 and x-axis is 6 sq. units, then m is equal to
The area of a region refers to the measurement of space within a boundary or enclosed area. In mathematics, it is often calculated using integration, especially when the boundary is curved or irregular. The area under curves represents accumulated quantities like distance, work or probability in various applications.
Class 12 Maths Chapter 8 Applications of Integrals is a crucial topic for the CBSE Exam 2024-25. It focuses on finding areas between curves and calculating volumes of solids using integration. The chapter has real-life applications in physics and engineering. Mastery of these concepts is important for solving practical problems and further studies.
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The given region is bounded by the lines y = mx, x = 1, x = 2, and the x-axis. The area enclosed by these boundaries is 6 square units.
The definite integral of mx from x = 1 to x = 2 gives us the area under the line y = mx, which is then used to calculate the value of m.
We solve the integral. We get the area as (3m/2). Therefore, we equate it to 6 and solve for m.
Solving
We multiply both sides by 2 to get 3m=12.
Divide it by 3, and thus we get m = 4.
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