Find f(x)d(x) if

Question

Find 9	f(x) dx
0

 if

f(x) =	7	for	x < 7
x	for	x ≥ 7

.

(It is supposed to be 7 for x < 7 and x for x ≥ 7)

Answer 1

So you'd break this up into two separate integrals, since f(x) is a piecewise function:

∫₀⁹ f(x)dx

∫₀⁷ f(x)dx + ∫₇⁹ f(x)dx

∫₀⁷ 7dx + ∫₇⁹ xdx

7x]₀⁷ + x²/2]₇⁹

7*7 - 7*0 + 81/2 - 49/2

49 + 32/2

130/2

So the answer is 130/2.