Integrating to find area: y=2 x^2 , y=8 x^2 , 5 x+y=3,x>=0

[AmySaunders]

The problem is copied and pasted below. I found the intersection points of the line and 8x^2 to be (3/8,9/8) and of the line and 2x^2 to be (1/2,1/2), so the area I am finding is shaped like a pointy comma. I integrated from 0 to 3/8 6x^2dx and added to it the integral from 3/8 to 1/2 (-5x+3-2x^2)dx, and obtained the answer 0.1589

To check my answer, I integrated with respect to y. Integral from 0 to 1/2 ((y/2)^1/2-(y/8)^1/2)dy + integral from 1/2 to 9/8 (((3-Y)/5)-(y/8)^1/2)dy.
This time my answer was 0.1588543769

Neither answer is correct. They aren't even equivalent. Can someone point out where I'm going wrong?



Sketch the bounded region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. (Do this on paper. Your instructor may ask you to turn in this graph.)

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[srmichael]

The problem is copied and pasted below. I found the intersection points of the line and 8x^2 to be (3/8,9/8) and of the line and 2x^2 to be (1/2,1/2), so the area I am finding is shaped like a pointy comma. I integrated from 0 to 3/8 6x^2dx and added to it the integral from 3/8 to 1/2 (-5x+3-2x^2)dx, and obtained the answer 0.1589

To check my answer, I integrated with respect to y. Integral from 0 to 1/2 ((y/2)^1/2-(y/8)^1/2)dy + integral from 1/2 to 9/8 (((3-Y)/5)-(y/8)^1/2)dy.
This time my answer was 0.1588543769

Neither answer is correct. They aren't even equivalent. Can someone point out where I'm going wrong?



Sketch the bounded region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. (Do this on paper. Your instructor may ask you to turn in this graph.)

=0" title="y=2 x^2 , y=8 x^2 , 5 x+y=3,x>=0" style="border: 0px; padding: 10px;">

What you did is correct. When you say the answer is "not correct", is it because you are maybe supposed to give the exact answer and not an approximate answer? The exact answer is 61/384 which is approximates to the 0.1589.

 

[AmySaunders]

Thank you, I should have tried that!