Question

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.

Answer 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