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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find 0 5 f ( x ) d x if

f ( x ) = { 3 for x < 3 x for x 3

To determine

To find: The value of the integral function 05f(x)dx.

Explanation

Given information:

The integral function is 05f(x)dx.

Here, the value of function f(x)=3 for x<3 and f(x)=x for x3.

Calculation:

Modify the integral function as given below.

05f(x)dx=03f(x)dx+35f(x)dx=I1+I2 (1)

Calculate the value of integral function I1 using the relation.

I1=03f(x)dx (2)

Here, x varies from 0 to 3.

Substitute 3 for f(x) in Equation (2).

I1=033dx=3[x]03=3(30)=9 (3)

Calculate the value of integral function I2 using the relation

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