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s asked in Science & MathematicsMathematics · 2 months ago

Evaluate the integrals for f(x) shown in the figure below...?

I mostly just want how to do a) explained to me. I tried to use A = 1/2 pi r^2 for the area and splitting the integral into a product of the int. of 3 from [0,2] and the int. of f(x) from [0,2], but no dice. What am I doing wrong here??? The multiplication of f(x) is really throwing me for a loop. Can I not just pull the 3 out of the integral and calculate the area using the normal formula?

a) Integral of 3*f(x) from [0, 2]

b) Integral of 3*f(x) from [0,6]

c) Integral of 2*f(x) from [1, 4]

d) Integral of abs(4*f(x)) from [1, 6]

Update:

Some (wrong) answers given: 

-3pi(0.5)^2

-3/2pi(0.5)^2

I'm just guessing at this point.

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  • 2 months ago
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    I don't really think "from" [0, 2] makes sense in the English language. It should be from 0 to 2, or ON [0, 2].

    You say you're integrating the 3 after pulling it out??? That's not right. Learn the rules of integration slowly and methodically.

    int k * f(x) dx =

    k * int f(x) dx

    if k is a real number independent of x.

    So calculate

    1) Integral of f(x) on [0, 2]

    2) Integral of f(x) on [0,6]

    3) Integral of f(x) on [1, 4]

    4) Integral of abs(f(x)) on [1, 6]

    Of course,

    1) is -pi/2

    2) is -pi/2 + 2pi

    3) is (1/2)(-pi/2) + (1/2)(2pi)

    4) is (1/2)pi/2 + 2pi (absolute value positivizes all the y-coordinates)

    Then multiply by 3, 3, 2, 4 in order to get a), b), c), d) respectively.

    In d) I used the fact that abs(4f(x)) = 4 abs(f(x)) for any f(x).

    • s2 months agoReport

      As it turns out I just can't read... yes, bad things happen when you're trying to integrate while angry. Anyway, I tried just plain pulling the 3 out (NOT integrating it) first but the problem is that I'm an idiot who can't read graph scales... thanks!

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