Homework Help

Evaluate the definite integral `int_(1)^8 (x + x^2)/(x^4) dx` .

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lizcnester | Student, Undergraduate | (Level 1) Honors

Posted August 3, 2012 at 5:18 PM via web

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Evaluate the definite integral `int_(1)^8 (x + x^2)/(x^4) dx` .

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 3, 2012 at 5:34 PM (Answer #1)

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The definite integral `int_(1)^8 (x + x^2)/(x^4) dx`

=> `int_(1)^8 1/x^3 + 1/x^2 dx`

=> `|-1/(2*x^2) - 1/x|_(1)^8`

=> `(-1/2)(1/64 - 1) - (1/8 - 1)`

=> `63/128 + 7/8`

=> `175/128`

The definite integral `int_(1)^8 (x + x^2)/(x^4) dx = 175/128`

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted August 3, 2012 at 5:35 PM (Answer #2)

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Evaluate `int_1^8(x+x^2)/x^4 dx` :

Rewrite as `int_1^8[x/x^4+x^2/x^4]dx` The integral of a sum is the sum of the integrals:

`=int_1^8x^(-3)dx + int_1^8x^(-2)dx`

`=-1/2x^(-2)|_1^8+(-1)x^(-1)|_1^8`

`=-1/2(1/64-1)-(1/8-1)`

`=175/128~~1.367`

The graph:

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The integral evaluates as 175/128

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