   Chapter 5.3, Problem 13QY ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Find an equation of the function f whose graph passes through the point (0, 1) and whose derivative is f ' ( x ) = 5 x x 2 + 16 4 .

To determine

To calculate: The equation of function f(x) that has derivative f(x)=5xx2+164 and whose graph passes through the point (0,1).

Explanation

Given Information:

The derivative of function f(x):

f(x)=5xx2+164

Formula used:

The power rule of integrals:

undu=un+1n+1+C (for n1)

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

The first derivative of function f(x):

df(x)dx=5xx2+164

Apply, integration on both sides:

df(x)dxdx=(5xx2+164)dx+C1f(x)=(5xx2+164)dx+C1

Consider the indefinite integral:

(5xx2+164)dx

Let u=x2+16, then derivative will be,

du=d(x2+16)=2xdx

Rewrite above indefinite integration as:

52(x2+164)2xdx

Substitute du for 2xdx and u for x2+16 in provided integration

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