Evaluate the integral in terms of areas.

1,823

Some tricks to help you:

a. count squares

b. calculate the area of known figures, such as triangles and rectangles.

For example, the integral in (b) can be calculate as the same of the area of a trapezoid($(1+3)\cdot 2/2$), a rectangle ($1\cdot 3$), and a triangle ($3\cdot 2/2$) to give a grand total of $10$.

That should cover it, good luck.

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Updated on August 01, 2022

Comments

  • etree
    etree over 1 year

    Image attached

    I understand that the first one is 4 from basically adding the squares inside the signed area, but I'm unsure on how to proceed in getting the other integrals. Any help would be appreciated, thank you.

    • Git Gud
      Git Gud over 8 years
      Can't you find the second one? Same principle.
    • Admin
      Admin over 8 years
      You are just finding the area under the graph on the given interval. It would probably help to divide it into triangles and rectangles.
    • etree
      etree over 8 years
      How am I supposed to add up the squares between 2 and 5? The ones in between 0 and 2 were either full squares or half squares.
    • Git Gud
      Git Gud over 8 years
      @etree Can you spot half a rectangle?
    • etree
      etree over 8 years
      Nevermind, I got it. Usage of triangles and trapezoids helped out Jake, thanks.
  • Mnifldz
    Mnifldz over 8 years
    While you're computing the values for the OP, you're not providing an explanation for how to compute those values.