# Antiderivatives in Calculus

Questions on the concepts and properties of antiderivatives in
calculus are presented. These questions have been designed to help you **better understand the concept and properties of antiderivatives**. In order to answer the questions below, you first need to review the definitions and theorems related to antiderivatives.

## Questions with Solutions

### Question 1

**True or False**. If F(x) is an antiderivative of f(x) and c is any constant, then F(x) + c is also an antiderivative of f(x).

__Answer :__True.

Differentiate F(x) + c.

### Question 2

**True or False**. If F(x) is an antiderivative of f(x), then

(1/c) F(c x) is an antiderivative of f(c x), where c is any non zero constant.

__Answer :__True.

Let u = c x and Differentiate (1 / c) F(c x) with respect to x

d/dx( (1 / c) F(c x) )

= (1 / c) d(u)/dx dF/du (chain rule)

= (1/c) c f(u) = f(c x)

### Question 3

**True or False**. An antiderivative of function f

**plus**an antiderivative of function g is an antiderivative of function f + g.

__Answer :__True. Use the rule of differentiation to differentiate F + G, where F is the antiderivative of f and G is the antiderivative of g, and see that you can get f + g.

### Question 4

**True or False**. An antiderivative of function f

**divided**by an antiderivative of function g is an antiderivative of function f / g.

__Answer :__False. Use the rule of differentiation to differentiate F / G, where F is the antiderivative of f and G is the antiderivative of g, and see that you cannot get f / g.

More references on calculus
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