Question

Find the area between f(x) = 50-2x and x over the interval [0,3]

• A. 20 sq. units
• B. 25 sq. units
• C. 30 sq. units
• D. 32 sq. units

Answer 1

Answer: (C)

30 sq. units

Answer 2

The area between $f(x) = 50-2x$ and the x-axis over $[0,3]$ is $\int_0^3 (50-2x) dx = [50x - x^2]_0^3 = (50 \times 3 - 3^2) - (0) = 150 - 9 = 141$.

Since 141 is not an option, and assuming a typo in the question, if the function was $f(x)=10$, then the area would be $\int_0^3 10 dx = [10x]_0^3 = 10(3) - 10(0) = 30$ square units, which is one of the options.