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 $x = 4$ ?

Question

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

?

Quantrex Academy · Accepted Answer

Correct answer: C. 32 square units

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 ∫_ 0 ^ 4 y \, dx Area = ∫_ 0 ^ 4 4x \, dx = [ 2x^2 ]_ 0 ^ 4 = 2(16) - 0 = 32 square units. Answer: 32 square units

Consider the following for the two (02) items that follow: The...

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