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1. If the integral from 1 to 6 of f of x, dx equals negative 10 and the integral from 3 to 6 of f of x, dx equals negative 8, then what is the value of integral from 1 to 3 of f of x, dx?

A. 2
B. -2
C. -18
D. 12

2. Use geometry to evaluate the integral from 0 to 6 of the function f of x, dx for f of x equals 4 for x less than or equal to 6 and equals the quantity 10 minus x for x greater than 6. (THIS IS THE ONE I NEED THE MOST HELP ON!!)

A. 4
B. 8
C. 16
D. 24

Thank you in advance! I really appreciate it :)

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2 answers

  1. 32 isn't one of the choices. Only those four

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  2. #1 break [1,6] into two intervals. It is easy to see that
    ∫[1,6] = ∫[1,3] + ∫[3,6]
    Now just plug in your numbers

    #2 I don't like any of the choices.
    Draw the graph, and you will see that you have a rectangle and a triangle, whose areas sum to 32

    Or, using your actual calculus, the area is
    ∫[0,6] 4 dx + ∫[6,10] 10-x dx
    = 4x[0,6] + 10x - x^2/2 [6,10]
    = 24 + (100-50) - (60-18) = 32

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