   Chapter 7.8, Problem 11SWU ### 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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# In Exercises 1-12, evaluate the definite integral. ∫ 0 2 x e x 2 + 1 d x

To determine

To calculate:

The value of the definite integral of xex2+1 with respect to dx over the limits 0 (lower limit) and 2 (upper limit)

Explanation

Given Information:

The function to be integrated with respect to dxisxex2+1 and the lower limit is 0 and upper limit is 2.

Formula used:

(1)  am+n=am×an

(2)  ddx(eax)=aeaxi.e[ddx(ax)]ax=aeax

(3)  ddx(ex2)=ddx(x2)ex2

(4)  dx=x

Step 1: Check the function given to integrate for the given limits is continues or not.

Step 2: If it is continues, find the anti-derivative of the given function.

Step3: Apply limits for the function obtained after integration

Calculation:

Given

02xex2+1dx

Let x2+1

Differentiate x2+1 with respect to t,

2xdx=dt

dx=dt2xxdx=dt2

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