Question

Select the correct expressions. Identify each expression and value that represents the area under the curve y = x + 4 on the interval (-3,2).

a) ∫₋₃² (x + 4) ,dx
b) ∫₂⁻³ (x + 4) ,dx
c) ∫₋₃² (4 - x) ,dx
d) ∫₂⁻³ (4 - x) ,dx

Answer 1

The correct expression to find the area under the curve y = x + 4 on the interval (-3,2) is option a, which is the definite integral of the function x + 4 from -3 to 2.

Step-by-step explanation:

The question requires finding the area under the curve y = x + 4 over the interval (-3,2). The correct mathematical expression for calculating this area is the definite integral of x + 4 with respect to x, from -3 to 2.

As per the given options:

• a. ∫₋₃² (x + 4) ,dx represents the area under the curve over the interval (-3,2), which is correct.
• b. ∫₂⁻₃ (x + 4) ,dx represents the area under the curve from 2 to -3, which is the negative of the area we want.
• c. ∫₋₃² (4 - x) ,dx is incorrect because the function inside the integral is not y = x + 4.
• d. ∫₂⁻₃ (4 - x) ,dx is also incorrect for the same reason as c, and also because the limits of integration are reversed.

Therefore, the correct expression that represents the area under the curve y = x + 4 on the interval (-3,2) is given by option a.