\( \int(x-2) d x= \) a. \( \frac{1}{2} x-2 x+C \) b. \( \frac{1}{2} x^{2}-2+C \) c. \( \frac{1}{2} x^{2}-2 x+C \) d. \( \frac{1}{2} x-2+C \)

To solve the integral \( \int(x-2) d x \), we apply the power rule of integration. The integral of \( x \) is \( \frac{1}{2} x^2 \), and the integral of a constant like \( -2 \) is simply \( -2x \). Thus, adding the constant of integration \( C \), we get: \[ \int(x-2) d x = \frac{1}{2} x^2 - 2x + C \] So, the correct answer is option c. Now, let's have some fun with this topic! Did you know that integrals are like a magic time machine for mathematicians? They allow us to find areas under curves, which can tell us a great deal about everything from physics to economics. Imagine figuring out how much paint you’d need to cover a sloped roof – that's where integrals come into play! And if you’re pondering where to dive deeper into the world of integrals, check out ‘Calculus Made Easy’ by Silvanus P. Thompson. It breaks down the complexities of calculus in a way that's super easy to digest, making it a classic for both beginners and seasoned learners alike!