Question

20 points! Does anyone know the answer to this?? Would be greatly appreciated if someone helped out :)

Answer 1

74.1

Explanation:

Lets split the integreal in accordance with f(x)

`\int\limits^9_7 {f(x)} \, dx = \int\limits^8_7 {f(x)} \, dx +\int\limits^9_8 {f(x)} \, dx\\\\= \int\limits^8_7 {(8x + 1)} \, dx +\int\limits^9_8 {(-0.4x + 9)} \, dx\\\\= 8\int\limits^8_7 {x} \, dx + \int\limits^8_7 {} \, dx - 0.4 \int\limits^9_8 {x } \, dx + 9\int\limits^9_8 {} \, dx\\\\= 9 [(x^2)/(2) ]^{^(8)}_{_(7)} + [x]^{^(8)}_{_(7)} -0.4[(x^2)/(2) ]^{^(9)}_{_(8)} + 9 [x]^{^(9)}_{_(8)}\\\\= 9 [(8^2 - 7^2)/(2) ] + [8-7] -0.4[(9^2 - 8^2)/(2) ] + 9[9-8]\\`

`= 9[(15)/(2) ] + 1 - 0.4[(17)/(2) ] + 9\\\\= (135)/(2) + 1 - (6.8)/(2) + 9\\\\=(128.2)/(2) + 10\\\\= 64.1 + 10\\\\= 74.1`