Question

If f is continuous on (a, b), then \(\frac{d}{{dx}}\left( {\int\limits_a^b {f(x)dx} } \right) = f(x)\)

Short answer

The given statement is FALSE.

Step-by-step solution

Step 1: Explanation

The given statement is FALSE

To apply the first fundamental theorem of calculus, the upper limit should have been x and not a constant. Since both the limits are constants, the indefinite integral is also a constant.

The final statement

Since the derivative of a constant is zero, the given statement is False.

Here is the restatement of the relevant theorem for those who forgot:

First Fundamental Theorem Of Calculus:

\(If F(x) = \int {{a^x}f(t)dt,\;then\;F'(x) = f(x)} \)