Given: f x = x , 0 ≤ x < 1 2 1 2 , x = 1 2 1 - x , 1 2 < x ≤ 1 and g x = x - 1 2 2 , x ∈ R . Then, the area (in sq. units) of the region bounded by the curves, y = f x and y = g x between the lines 2 x = 1 and 2 x

Question

Given: f x = x , 0 &#8804; x &#60; 1 2 1 2 , x = 1 2 1 - x , 1 2 &#60; x &#8804; 1 and g x = x - 1 2 2 , x &#8712; R . Then, the area (in sq. units) of the region bounded by the curves, y = f x and y = g x between the lines 2 x = 1 and 2 x = 3 , is:

Quantrex Academy · Accepted Answer

Correct answer: B. 3 4 - 1 3

Required area = Area of trapezium ABCD - &#8747; 1 / 2 3 / 2 x - 1 2 2 d x = 1 2 3 - 1 2 1 2 + 1 - 3 2 - 1 3 x - 1 2 3 1 2 3 2 = 3 4 - 1 3

Given: f x = x , 0 ≤ x < 1 2 1 2 , x = 1 2 1 - x , 1 2 < x ≤ 1 and g x = x - 1 2 2 , x ∈ R . Then, the area (in sq. units) of the region bounded by the curves, y = f x and y = g x between the lines 2 x = 1 and 2 x = 3 , is:

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Correct answer

Step-by-step solution

More from Area Under Curves

Given: f x = x , 0 &#8804; x &#60; 1 2 1 2 , x = 1 2 1 - x , 1 2 &#60; x &#8804; 1 and g x = x - 1 2 2 , x &#8712; R . Then, the area (in sq. units) of the region bounded by the curves, y = f x and y = g x between the lines 2 x = 1 and 2 x = 3 , is:

Options

Correct answer

Step-by-step solution

More from Area Under Curves

Given: f x = x , 0 ≤ x < 1 2 1 2 , x = 1 2 1 - x , 1 2 < x ≤ 1 and g x = x - 1 2 2 , x ∈ R . Then, the area (in sq. units) of the region bounded by the curves, y = f x and y = g x between the lines 2 x = 1 and 2 x = 3 , is: