Question

What is the area between the curves x = |y| and x = -y² from y = 0 to y = 3?

a) 9 square units
b) 12 square units
c) 18 square units
d) 27 square units

Answer 1

To find the area between the curves x = |y| and x = -y² from y = 0 to y = 3, calculate the integral of the difference between the two curves.

Step-by-step explanation:

To find the area between the curves x = |y| and x = -y² from y = 0 to y = 3, we need to find the integral of the difference between the two curves. Since the curve x = -y² is always below the curve x = |y| in the given interval, we subtract the equation of the curve x = -y² from the equation of the curve x = |y|. The integral gives us the area between the curves.

The integral of x = |y| - x = -y² from y = 0 to y = 3 is:

∫(|y| - (-y²)) dy from 0 to 3

Simplifying this integral will give us the area between the curves.