# The value of f(4)

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 5.4, Problem 25E
To determine

## To find: The value of f(4)

Expert Solution

The value of f(4) is 29

### Explanation of Solution

Given information: f(1)=12, f is continuous, and 14f(x) dx=17

Let’s remind of the fundamental theorem of calculus part 2:

Let G(x) be any function which is defined and continuous on [a, b] and which is also differentiable and obeys G(x) = f(x) for all a < x < b . Then abf(x)dx = G(b) - G(a) or abG(x) dx = G(b) - G(a)

Since ,  x, f(x)=f(x) f is primitive function of f '(x)

Therefore,

14f(x) dx=17

From fundamental theorem,

f(4)-f(1)=17

f(4)=17+f(1)f(4)=17+12

f(4)=29

Thus, f(4)=29

Hence, The value of f(4) is 29 .

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