BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 5.2, Problem 46E
To determine

To evaluate : 13(2ex1)dx

Expert Solution

Answer to Problem 46E

  13(2ex1)dx=2e(e21)

Explanation of Solution

Given information : f(x)=2ex1,   where a=1,b=3

Formula used : abf(x)dx=limx(ban)i=1nf(xi) 

Calculation :

   We have, x= 31 n = 2 n   Here, x 0 =1

   x 1 =1+ 2 n , x 2 =1+ 4 n , x 3 =1+ 6 n ,............... x i =1+ 2i n

   1 3 ( 2 e x 1 )dx= lim x 2 n i=1 n ( 2 e ( 1+ 2i n ) 1 )

   = lim x 2 n i=1 n ( 2 e ( 1+ 2i n ) 2 )

   1 3 ( 2 e x 1 )dx= lim x 4 n i=1 n e 1+ 2i n 2     ..............................( 1 )

   Now, i=1 n e 1+ 2i n =[ e 3n+2 n e n+2 n e 2 n 1 ]

   Equation ( 1 ) becomes,

   1 3 ( 2 e x 1 )= lim x 4 n [ e 3n+2 n e n+2 n e 2 n 1 ] = lim x 2[ e 3n+2 n e n+2 n e 2 n 1 2 n ]=2( e 3 e )=2e( e 2 1 )

Therefore, 13(2ex1)dx=2e(e21)

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