   Chapter 6.2, Problem 6CP ### 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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# Checkpoint 6Use Example 6 to find the probability that a participant will recall between 0% and 62.5% of the material.

To determine

To calculate: The probability of recalling between 0% and 62.5%, when probability of recalling between a% and b% is modelled as P(axb)=ab1e2x2exdx.

Explanation

Given Information:

The provided expression is,

P(axb)=ab1e2x2exdx

Formula used:

(1) The formula 38 for integral uneudu is:

uneudu=uneunun1eudu

(2) The formula 37 for integral ueudu is:

ueudu=(u1)eu+C

(3) General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=x.

Differentiate the considered function with respect to x using power rule of differentiation.

du=dx

Consider the provided expression:

P(axb)=ab1e2x2exdx

Rewrite.

P(axb)=1e2abx2exdx

Here, n=2, u=x and du=dx.

Substitute x=u, 2=n, and dx=du,

P(axb)=1e2abuneudu

Use the formula 38 and solve the above integral as:

P(axb)=1e2[uneunun1eudu]ab

Substitute x for u, and 2 for n

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