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- 964dxx2 - 64X°-oo

Question

Can somebody help me on how to evaluate the integral.

 

 

- 9
64
dx
x2 - 64
X°
-oo
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- 9 64 dx x2 - 64 X° -oo

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Step 1

Refer to the question, first evaluate the given integral in indefinite form that is with the limits.

64
-dx (64sx2 -64dt)
x264
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64 -dx (64sx2 -64dt) x264

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Step 2

Now use partial differentiation to solve the integration.

So the formula of partial fraction decomposition of given integral is,

1
1
x-64 x8(x +8)
Then Partial fraction decomposition,
1
B
A
(x-8)(x+8) x-8 x+8
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1 1 x-64 x8(x +8) Then Partial fraction decomposition, 1 B A (x-8)(x+8) x-8 x+8

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Step 3

Now find the value of A and...

1
В
A
(х-8)(х+8)
х - 8
x +8
As,denominator are equal, So equate the numerator
А(х +8) В(x-8)
1
(x-8)(x+8)
х -8
1%3D A(х +8)+ B(х-8)
1 xABx 8A -8B
1 (A B)x8.A -8B
help_outline

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1 В A (х-8)(х+8) х - 8 x +8 As,denominator are equal, So equate the numerator А(х +8) В(x-8) 1 (x-8)(x+8) х -8 1%3D A(х +8)+ B(х-8) 1 xABx 8A -8B 1 (A B)x8.A -8B

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Math

Calculus

Integration

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