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What is the area of the region bounded by |x| < 5, y = 0 and y = 8?

What is the area of the region bounded by |x| < 5, y = 0 and y = 8? Correct Answer 80 square units

Concept:

|x| < a ⇒ - a < x < a

Equation of x-axis is given by: y = 0

If y = a ≠ 0 and a > 0 , then y = a represents the equation of line parallel to x-axis and lying above the x-axis.

If y = a ≠ 0 and a < 0, then y = a represents the equation of line parallel to x-axis and lying below the x-axis.

Calculation:

Given: |x| < 5, y = 0 and y = 8

By plotting the above equations and in equation on the co-ordinate plane as shown in the figure below:

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The shaded portion represents the region bounded by the given equations and in equation.

As we can see that the bounded region is a rectangle with length l = 10 units and breadth b = 8 units.

⇒ The area of the bounded region = l × b = 10 × 8 = 80 sq. units

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