   Chapter 7.8, Problem 10SWU ### 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. ∫ 2 e 1 y − 1 d y

To determine

To calculate:

The value of the definite integral of 1y1 with respect to dy over the limits 2 (lower limit) and e (upper limit)

Explanation

Given Information:

The function to be integrated with respect to dyis1y1 and the lower limit is 2 upper limit is e.

Formula used:

ddx(constant)=0dxx=lnx

abf(x)dx=F(x)|ba=F(b)F(a)

[F(x)is antiderivation of f(x)]

The following is procedure for finding definite integration (i.e, with limits)

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

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

Step3: Sum of the integration from lower limit till the point of discontinuity and from the point of discontinuity to upper limit.

Step 4: Apply limits for the function obtained after integration.

Calculation:

Consider the provided information,

2e1y1dy

[1y1iscontiniousforallyRexceptat1]

Let y1=z

y=z+1 …… (1)

Differentiate (1) with respect to z

dydz=1dy=dz …… (2)

Limit 2 changes to 1 [z=y1]

Limit e changes to e1[z=y1]

Now, solve the integrat

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