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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Checkpoint 5 Worked-out solution available at LarsonAppliedCalculus.com

Evaluate 0 5 | x 2 | d x .

To determine

To calculate: The value of integral 05|x2|dx.

Explanation

Given information:

The integral is 05|x2|dx.

Formula used:

According to the integration sum rule for two continuous functions f and g on close interval [a,b]:

ab[f(x)±g(x)]dx=abf(x)dx±abg(x)dx

According to the fundamental theorem of calculus.

abf(x) dx=F(b)F(a)

For a function F when F(x)=f(x) and function f is continuous on [a,b].

Calculation:

Consider the integral,

05|x2|dx

As it is known by the definition of absolute value,

|x|={x, x<0  x, x0}

Apply the absolute value definition,

|x2|={(x2), x<2  (x2), 

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