What is the area bounded by the curve, the x-axis and the line x=4?
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.
- A. 8 square units
- B. 16 square units
- C. 32 square units ✓
- D. 64 square units
Correct Answer: C. 32 square units
Explanation
The curve is the line y = 4x. The area bounded by this line, the x-axis, and x = 4 is given by the integral \int_0^4 4x \, dx = [2x^2]_0^4 = 2(16) - 0 = 32 square units.
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