Question

given
Determine whether the
or divergent.
integral e power x
dx is convergentor divergent​

Answer 1

Answer:

he was the only person who was able and was the first to be in a new position for a long term and water and a very long term plan to the United nations that we had in a relationship that

Answer 2

Answer:

Explanation:

First focusing on the integral without bounds:

∫

e

1

x

x

3

d

x

Let

t

=

1

x

this implies that

d

t

=

−

1

x

2

d

x

, so the integral can be rewritten as:

=

−

∫

e

1

x

(

1

x

)

(

−

1

x

2

)

d

x

=

−

∫

t

e

t

d

t

Performing integration by parts, letting:

{

u

=

t

==⇒

d

u

=

d

t

d

v

=

e

t

d

t

==⇒

v

=

e

t

=

−

(

t

e

t

−

∫

e

t

d

t

)

=

−

e

t

(

t

+

1

)

=

e

1

x

(

1

−

1

x

)

So:

∫

1

0

e

1

x

x

3

d

x

=

e

1

x

(

1

−

1

x

)

∣

∣

∣

∣

1

0

=

e

(

1

−

1

)

−

lim

x

→

0

+

e

1

x

(

1

−

1

x

)

As

x

→

0

,

1

x

→

∞

and

e

1

x

→

∞

. Together, the limit will also be

∞

, so the integral diverge