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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

The following exercises are intended only for those who have already covered Chapter 6.

Evaluate the integral.

1 9 1 2 x   d x

To determine

To evaluate:

1912xdx

Explanation

1)  Concept:

The Fundamental Theorem of Calculus: Suppose f is continuous on [a, b], then

abfxdx=Fb-F(a), where F is antiderivative of f, that is F'=f.

2) Formulae:

i) anti derivative of 1x=ln x+C

ii)  alnb=lnba

3) Calculations:

Consider,

1912xdx

By taking 12 outside the integral

1912xdx=12191xdx

By applying formula (i) and using the Fundamental Theorem of Calculus

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