Integrals 4-Calculus-Quiz Solution, Exercises of Calculus

Prof. Maitreya Sawhney took quiz for Calculus during class at Chennai Mathematical Institute. This is solution he provided latter. It includes: Integral, Variables, First, Order, Integrate, Trignometric, Function, Respect, Time

Typology: Exercises

2011/2012

Uploaded on 07/20/2012

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Name: Solution Registration Number: Solution
Quiz No. 8
Calculus-I Section-4
=====================================================================
Problem: Evaluate the integral
.
ln2
1
dx
xx
Solution:
Let
dx
xx
Iln2
1
dx
x
xI 1
.)][ln(
2
12
1
Notice that
x
x
dx
d1
)ln(
dxx
dx
d
xI )ln(.)][ln(
2
12
1
C
n
xf
dxxfxfC
x
In
n
1
)]([
)()]([
2
1
)][ln(
2
11
/
2
1
.)ln( CxI
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Name: Solution Registration Number: Solution

Quiz No. 8

Calculus-I Section-

Problem: Evaluate the integral

2 ln

dx

x x

Solution:

Let

dx x x

I

2 ln

   dx x

I x

[ln( )]. 2

2

1

Notice that

x

x dx

d 1 ln( )

   xdx dx

d I [ln( x )]. ln( ) 2

2

1

C n

f x C f x f xdx

x I

n n

1

[ ( )]

[ ( )] ( )

[ln( )]

1 /

2

1

I  ln( x ) C.

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