Question

What is an integrand?
(a) The symbol $dx$
(b) The function $f\left( x \right)$ to be integrated
(c) The interval $\left[ a,b \right]$
(d) None of these

Answer 1

Hint: We will recall the definition of an integral. We will look at the notation for writing integrals. There are two types of integrals and there is a relation between these two types. The part which is the integrand in the notation of both these types is the same.

Complete step-by-step answer:
The integral is also called the antiderivative. There are two reasons to study integration. One reason is to find the function whose derivative is given. The other reason is to find the area bounded by the graph of a function under certain conditions. There are two types of integrals, definite integral and indefinite integral. These two types of integrals are related to each other by the Fundamental theorem of Calculus. We know that the indefinite integral of a function $f\left( x \right)$ is written in the following manner,
$I=\int{f\left( x \right)dx}$.
And the definite integral is written as follows,
$I=\int\limits_{a}^{b}{f\left( x \right)dx}$.
The above expressions denote the integral of $f$ with respect to $x$. The function $f\left( x \right)$ is called the integrand in both of these expressions.

So, the correct answer is “Option b”.

Note: It is necessary that we understand the definitions or concepts before using them in calculations. The reasons for studying integration make it straightforward to understand the use of integration. Integration is a very important part of mathematics and is related to many other areas in mathematics. It has applications in other subjects like physics and engineering sciences, etc.