Answer to Question #199525 in Calculus for nela

Question

if f is continuous for all x and, ∫ f(x)dx and ∫b/a f(x) dx are equal which one of the following statement is correct, 1. the function f is the constant e ,2. the function f is not differentiable, 3. the function f is the constant 0 , 4. the function f is any arbitrary constant c ,5. the function f is the identity function

Answer 1

We have given the statement that,

$f$ is continuous for all x

$\int f(x)dx = \dfrac{b}{a}\int f(x)dx$

Then, the function $f$ is the constant