Math involving integrals between curves

Question

Find the area of the region in the 𝑥𝑦xy-plane bounded above by the graph of the function 𝑓(𝑥)=(8/17)𝑥−(64/17)f(x)=(8/17)x−(64/17), below by the 𝑥x-axis, on the left by the line 𝑥=8x=8, and on the right by the line 𝑥=25x=25. The area is

Answer 1

Area A = ∫₈²⁵(8x/17 - 64/17)dx = (4x²/17 - 64/17x)₈²⁵ = 4/17((625 - 64) - 16(25 - 8)) = 68