Question

What is wrong with the equation ?

∫₋₃¹ x⁻³ dx = x⁻²/-1]₋₃¹ =-4/9
a. there is nothing wrong with the equation
b. f(x) x⁻³ is continuous on the interval [-3,1] so FTC2 cannot be applied
c. the lower limit is less than 0, so FTC2 sannot be applied
d. f(x)=x⁻³ is no continuous on th einterval [-3,1] so FTC2 cannot be applied
e, f(x)=x⁻³ is no continuous at x =-3, so FTC2 cannot be applied

Answer 1

The equation's mistake is in the integration process; f(x) = x^-3 is not continuous at x = 0, so the Fundamental Theorem of Calculus Part 2 cannot be directly applied to the interval [-3,1].

Step-by-step explanation:

The integral provided in the question is ∫₋₃¹ x⁻³ dx, which evaluates to x⁻²/-1 |₋₃1. The issue with the equation lies in the integration process. The function f(x) = x⁻³ is not continuous on the interval [-3,1] because it is undefined at x = 0.

Hence, the Fundamental Theorem of Calculus Part 2 (FTC2) cannot be applied directly over the entire interval without addressing the discontinuity at x = 0.

The correct approach to evaluate the integral is to break it into two intervals where the function is continuous: from -3 to a point approaching 0, and from a point approaching 0 to 1.