# use part 1 of the fundamental theorem of calculus to find the derivative of the function.

### 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 10E
To determine

## To find: use part 1 of the fundamental theorem of calculus to find the derivative of the function.

Expert Solution

The derivative of the function is g(r)=r2+4

### Explanation of Solution

Given information: The function is g(r)=0rx2+4 dx

Calculation: Let’s remind of the fundamental theorem of calculus part 1:

The fundamental theorem of calculus part 1: If f is continuous on [a,b] then the function of g defined by

g(x)=axf(t) dt where axb is continuous on [a,b] and differentiable on (a,b) and g(x)=f(x) .

Now given, g(r)=0rx2+4 dx

Differentiation with respect to r,

ddrg(r)=ddr[0rx2+4 dx]

g(r)=r2+4 [ where g(r)=f(r) ]

Thus, g(r)=r2+4

Hence, The derivative of the function is g(r)=r2+4 .

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