Question

Notice that this last integral is the same as the integral we started with. Treat this like an equation and move the integral to the left-hand side:

a) ( int f(x) ,dx = int g(x) ,dx )
b) ( int f(x) ,dx - int g(x) ,dx = 0 )
c) ( int f(x) ,dx + int g(x) ,dx = 0 )
d) ( int f(x) ,dx ⋅ int g(x) ,dx = 0 )

Answer 1

The correct choice is option b) which represents an integral equation indicating that the area under the curves of f(x) and g(x) is the same, thereby making their difference zero.

Step-by-step explanation:

The question appears to revolve around solving an integral equation where the integral of a function f(x) equals the integral of another function g(x). When the two integrals equal each other, if we set them on opposite sides of an equation, their difference is zero. Therefore, the correct answer is option b), which states (int f(x) ,dx - int g(x) ,dx = 0). This implies that the area under the curve of f(x) is identical to the area under the curve of g(x) over the same interval, thus making their difference zero.