Final answer:
The integral of 2/5 - 2x is found by integrating each term individually. The result is (2/5)x - x^2 + C, where C is the constant of integration.
Step-by-step explanation:
To find the integral of the function 2/5 - 2x, we approach it as a simple indefinite integral problem. We integrate each term separately, following the basic principles of integration. For constants, the integral is just the constant times the variable of integration. For the x term, we use the power rule for integration, which in general states that the integral of xndx is xn+1/(n+1), provided that n is not equal to -1. Let's apply these rules step-by-step:
- Integral of 2/5: Since 2/5 is a constant, its integral is (2/5)x.
- Integral of -2x: This is an x term where n=1. Apply the power rule to get the integral of x, which is x2/2. So the integral of -2x is -2(x2/2), simplifying to -x2.
Combining both terms, the integral of 2/5 - 2x is (2/5)x - x2 + C, where C represents the constant of integration.