Intergral from -2 to 2 (-2 is at the bottom of the integral sign and 2 is at the top) x^-2dx = -x^-1] (the bracket has a 2 at the top and -2 at the bottom) = -(2)^-1-(-(-2)^-1) = (-1/2)-(1/2 = -1
Is this true or false. I think it's false, but can someone explain to me why it's false.
To determine if the given statement is true or false, we can evaluate the integral and check if it matches the given result.
Let's solve the integral step by step:
∫[from -2 to 2] x^(-2) dx
First, let's rewrite the integral in a different form:
∫[from -2 to 2] 1/x^2 dx
Now, we can integrate using the power rule for integrals:
∫[from -2 to 2] 1/x^2 dx = [-1/x] [from -2 to 2]
Applying the limits of integration:
[-1/2] - [-1/-2]
Simplifying:
-1/2 + 1/2
The result is 0, not -1. Therefore, the given statement is false.