Consider the following for the two (02) items that follow: The slope of the tangent to the curve y = f(x) at (x, f(x)) is 4 for every real number x and the curve passes through the origin. What is the area bounded by the curve, the x -axis and the line x = 4 ?

Step-by-step solution

Given dy dx = 4 Integrating both sides, y = 4x + C Since the curve passes through the origin (0,0) , we have 0 = 4(0) + C C = 0 The equation of the curve is y = 4x The area bounded by the curve, the x -axis and the line x = 4 is given by ₀⁴ y , dx Area = ₀⁴ 4x , dx = [ 2x^2 ]₀⁴ = 2(16) - 0 = 32 square units. Answer: 32 square units