Final answer:
The integral of a constant function such as 7 with respect to x is 7x plus a constant of integration, represented as 7x + C.
Step-by-step explanation:
The question asks about the process of integration, specifically how to find the integral of a constant function. From the given information, d/dx (7x) = 7, which indicates that the derivative of 7x with respect to x is 7. This implies that when we integrate 7 with respect to x, we should get the original function 7x (up to a constant). The process of finding the integral is the reverse of differentiation, often referred to as antidifferentiation.
To find the integral ∠7 dx, we look for a function whose derivative is 7. Since the derivative of x with respect to x is 1, we can multiply x by 7 to get a function 7x, which provides a derivative of 7 when differentiated with respect to x. Therefore, the integral of 7 with respect to x is:
∠7 dx = 7x + C
where C is the constant of integration which represents any constant value that could have been present in the original function before differentiation.