Question

What is the area bounded by the pair of curves y=x² −8x and y=8x−1?

A) 58 square units
B) 64 square units
C) 72 square units
D) 80 square units

Answer 1

To find the area bounded by the curves y=x² -8x and y=8x-1, set the equations equal to each other to determine the points of intersection, compute the integral of their difference, which results in an area of 64 square units.

Correct option is B) 64 square units

Step-by-step explanation:

The area bounded by the pair of curves y=x² − 8x and y=8x− 1 is found by computing the integral of the difference between the two functions over the interval where they intersect.

1. First, set the two functions equal to each other to find the points of intersection: x² − 8x = 8x − 1.
2. Solve for x to find the intersection points, which turn out to be x = 1 and x = 9.
3. Next, calculate the integral of the difference between the functions (8x − 1) - (x² − 8x) from x = 1 to x = 9.
4. The resulting integral is the area between the curves, which is 64 square units.