   Chapter 5.4, Problem 32E ### 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
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# Evaluating a Definite Integral In Exercises 17-38, evaluate the definite integral. See Examples 3 and 4. ∫ 0 2 x 1 + 2 x 2 d x

To determine

To calculate: The value of definite integral 02x1+2x2dx.

Explanation

Given Information:

The integral is 02x1+2x2dx.

Formula used:

The fundamental theorem of calculus states that,

If f is integrable on interval [a,b] then abf(x)dx=F(b)F(a).

The integration formula is xndx=xn+1n+1+C.

Calculation:

Consider the integral,

02x1+2x2dx

The integral in the radical form can be written as,

02x1+2x2dx=02x(1+2x2)1/2dx

Multiply and divide by 4,

02x(1+2x2)1/2dx=02x(1+2x2)1/2(4)dx4

Now use the substitution procedure,

1+2x2=u4x=d(u)dx4xdx=du

The lower limit is,

1+2x2=u1+2(0)2=uu=1

The upper limit is,

1+2x2=u1+2(2)2=u

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