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Thread: Intergrals (sums and differences in area)

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    V_L
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    Intergrals (sums and differences in area)

    Hi,

    Im sorry i know this is a shit load of questions but I've been struggling all afternoon with them so any help would be greatly appreciated!! )

    9. Find the area enclosed between the curve y = x 3 , the x -axis and the line y = -3 x + 4

    10. Find the area enclosed by the curves y = ( x - 2)^2 and y = ( x - 4)^2 .

    11. Find the area enclosed between the curves y = x^2 and y = x^3 .

    12. Find the area enclosed by the curves y = x^2 and x = y62 .

    13. Find the area bounded by the curve y = x^2 + 2 x - 8 and the line y = 2 x + 1.

    14. Find the area bounded by the curves y = 1 - x^2 and y = x^2 - 1.

    15. Find the exact area enclosed between the curve y = √(4 − x^2) and the line x - y + 2 = 0.

    Answers:

    9. 0.42 units^2
    10. ⅔ units^2
    11. 1/12 units^2
    12. ⅓ units^2
    13. 36 units^2
    14. 2⅔ units^2
    15. (π - 2) units^2
    Last edited by V_L; 27 Mar 2017 at 10:03 PM.

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    Re: Intergrals (sums and differences in area)

    Q9) The 2 curves y = x^3 and y = -3x + 4 meet at x = 1. The reqd area is made up of 2 parts: the area under the 1st curve from x = 0 to x = 1; the 2nd part is the area under the straight line from x = 1 to x = 4/3. Therefore reqd area:

    Last edited by Drongoski; 26 Mar 2017 at 7:44 PM.
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    Re: Intergrals (sums and differences in area)

    Q10) The 2 curves intersect at x = 3 and touch the x-axis at x= 2 and x = 4 resp. The reqd area is made up of 2 parts (by symmetry, each of same area)
    Last edited by Drongoski; 26 Mar 2017 at 7:57 PM.
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    Re: Intergrals (sums and differences in area)

    Quote Originally Posted by V_L View Post
    Hi,

    Im sorry i know this is a shit load of questions but I've been struggling all afternoon with them so any help would be greatly appreciated!! )

    9. Find the area enclosed between the curve y = x 3 , the x -axis and the line y = -3 x + 4

    10. Find the area enclosed by the curves y = ( x - 2) 2 and y = ( x - 4) 2 .

    11. Find the area enclosed between the curves y = x 2 and y = x 3 .

    12. Find the area enclosed by the curves y = x 2 and x = y 2 .

    13. Find the area bounded by the curve y = x 2 + 2 x - 8 and the line y = 2 x + 1.

    14. Find the area bounded by the curves y = 1 - x 2 and y = x 2 - 1.

    15. Find the exact area enclosed between the curve y = 4 − x2 and the line x - y + 2 = 0.

    Answers:

    9. 0.42 units^2
    10. ⅔ units^2
    11. 1/12 units^2
    12. ⅓ units^2
    13. 36 units^2
    14. 2⅔ units^2
    15. (π - 2) units^2












    Last edited by 1729; 26 Mar 2017 at 8:12 PM.
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    Re: Intergrals (sums and differences in area)

    Hi, Thank you so so much!! Could you please explain how Q10 works please? Also i made a mistake on question 15, one of the equations was meant to be y = the square root of (4-x^2) so thats why the answers don't match

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    Re: Intergrals (sums and differences in area)

    Quote Originally Posted by V_L View Post
    Hi, Thank you so so much!! Could you please explain how Q10 works please? Also i made a mistake on question 15, one of the equations was meant to be y = the square root of (4-x^2) so thats why the answers don't match
    Last edited by 1729; 27 Mar 2017 at 11:49 PM.
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    Re: Intergrals (sums and differences in area)

    Last edited by 1729; 9 Apr 2017 at 5:03 PM.
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