Evaluate ` int_1^8(x+x^2)/(x^4) dx`It should be Evaluate ʃ (superscript 8)(subscript 1) (x+x^2)/(x^4) dx. Include a corresponding sketch.

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

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

To simplify, express the integrand as two fractions.

`=int_(1)^(8) (x/x^4+x^2/x^4)dx = int_(1)^8( 1/x^3+1/x^2)dx`

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

Then, apply the power formula of integral which is `int u^ndu=u^(n+1)/(n+1) + C` .

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

`= -1/x^2 - 1/x|_1^8`

`= 175/128=1.37`

The graph of the integral is:

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`int_(1)^(8) (x+x^2)/x^4dx` is the region bounded by the four curves `y=(x+x^2)/x^4` , `x=1` and `x=8`  and `y=0` .

And the area bounded by the four curves is: `int_(1)^(8) (x+x^2)/x^4dx =1.37` .

rtaylor13 | Student, Undergraduate | (Level 1) eNoter

Posted on

I think the person above used the wrong scripts...

Also I realized I wrote the scripts wrong anyway. It should be Evaluate ʃ (superscript 8)(subscript 1) (x+x^2)/(x^4) dx. Include a corresponding sketch.