Question

Evaluate the definite integral: ∫(5x^(-2) - 6) dx from 1 to 3.

Answer 1

The value of the definite integral ∫(5x^(-2) - 6) dx from 1 to 3 is 50/3 after finding the antiderivatives of the integrand and substituting the limits.

Step-by-step explanation:

To evaluate the definite integral ∫(5x^(-2) - 6) dx from 1 to 3, we need to find the antiderivatives of the given function and then apply the Fundamental Theorem of Calculus by calculating the difference between the values of the antiderivative at the upper and lower limits of integration.

1. Find the antiderivative of 5x^(-2) - 6. The antiderivative of 5x^(-2) is -5/x, and the antiderivative of 6 is 6x.
2. Substitute the limits of integration into the antiderivative, which gives us (-5/3 + 18) - (-5 + 6).
3. Simplify the expression to find the value of the integral.

The calculation would give us (-5/3 + 18) - (-5 + 6) = -5/3 + 18 + 5 - 6 = -5/3 + 17, which simplifies to 16 2/3 or 50/3. Therefore, the value of the integral is 50/3.