Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

What is the integration?

Attachment image

4 Answers

Relevance
  • rotchm
    Lv 7
    1 month ago
    Favorite Answer

    Hints: Recalling your high school algebra, rewrite your integrand 

    as y^(-1/2) - y^(1/2).

    Agree?

    Now, since you know how to integrate yⁿ , the most basic integral you learned, 

    just integrate the above. What do you get?

    Surely you can take it from there?

    If not, ask for further help. 

    Another hint: its very impolite and unnecessary here to be anon. 

    Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them. 

  • Vaman
    Lv 7
    1 month ago

    It is the total area under the curve.

  • JOHN
    Lv 7
    1 month ago

    Integrand is y^(-1/2) – y^(1/2)

    Indefinite integral is 2y^(1/2) – (2/3)y^(3/2)

    Definite integral is (4 – (2/3)(8) – (2 – 2/3) = -4/3 – 4/3  = -8/3.

  • 1 month ago

    4

    ∫ (1 - y)/√y dy =

    1

    4

    ∫ y^(-1/2) - y^(1/2) dy =

    1

    ................................4

    2y^(1/2) - 2y^(3/2)/3 | =

    ................................1

    2(4^(1/2)) - 2(4^(3/2))/3 - [2(1^(1/2)) - 2(1^(3/2))/3] =

    4 - 16/3 - [2 - 2/3] =

    12/3 - 16/3 - 6/3 + 2/3 =

    -8/3

Still have questions? Get your answers by asking now.