Question

Test the convergence of integration of 0 to 1 DX/x^2√1-x

Answer 1

Answer:

Step-by-step explanation:

Making  

x

=

sin

y

with  

d

x

=

cos

y

d

y

and substituting into the integral

I

=

∫

x

d

x

√

1

−

x

2

≡

∫

(

sin

y

cos

y

)

cos

y

d

y

=

∫

sin

y

d

y

=

−

cos

y

The integration limits are changed to

x

=

0

→

y

=

0

x

=

1

→

y

→

π

2

so

I

=

−

cos

(

π

2

)

−

(

−

cos

(

0

)

)

=

1