math

Let f of x equals 4 for x less than or equal to 3 and equals the quantity 7 minus x for x greater than 3. Use geometric formulas to evaluate the integral from x equals 1 to x equals 7 of f of x, dx.

I got 16 but i dont think it is right.

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  1. ever think of using math notation instead of words?

    f(x) =
    4x for x <= 3
    7-x for x > 3

    ∫[1,7] f(x) dx
    = ∫[1,3] 4x dx + ∫[3,7] 7-x dx
    = 2x^2[1,3] + 7x - x^2/2 [3,7]
    = [(2*3^2)-(2*1^2)]+[(7*7-7^2/2)-(7*3-3^2/2)]
    = 16+8
    = 24

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