The correct answer is option (b) False.
Differentiation:
Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure for determining the instantaneous rate of change of a function depending on one of its variables.
Explanation:
Given:
A statement is given "If f is continuous on
[a,b], then ddx(∫baf(x)dx)=f(x)".
The objective of the question is to determine whether the statement is true or false and why.
It is known that the value of a definite integral of a function is always a constant. So, ∫baf(x)dx
is a constant.
It is also known that the derivative of a constant is always equal to 1. Therefore, the correct equation is ddx(∫baf(x)dx)=1.
Thus, the given statement is false.
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