solve this?

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  • Anonymous
    1 month ago

    Given: a→b∫ f(x) dx = 3 and c→b∫ f(x) dx = 5

    If c→b∫ f(x) dx = 5 then

    b→c∫ f(x) dx = -5

    a→c∫ f(x) dx = [a→b∫ f(x) dx] + [b→c∫ f(x) dx]

    a→c∫ f(x) dx = [3] + [-5] = -2

  • 1 month ago

    The question has errors:

    ‘dx’ is missing from each integral.

    The instructions make no sense.

    7 marks for a single question you can do in your head is silly.

    ____________________________

    Each integral has the lower limit on the bottom.  So we can tell a<b, c<b and a<c.

    That means the limit values in increasing order are: a, c, b.

    Imagine points on the x-axis, left to right: x=a, x=c, x=b

    Each integral is equal to the area under the f(x) curve between the given limits.  So we know:

    (area from a to c) + (area from c to b) = (area from a to b)

    (area from a to c) = (area from a to b) - (area from c to b)

    . . . . . . . . . . . . . . .=  3 – 5 = -2

    (The negative sign idicates area below the x-axis)

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