Question

Please answer all questions

Answer 1

Hi,

Explanation:

1)

y''=7 cos(x)

=> y'= 7 sin(x)+C

=> y=-7 cos(x)+Cx+D

y'(0)=9 => 9=7*0+C => C=9

y(0)=-9 => -9=-7*1+9*0+D => D=-2

y= 7 cos(x) +9x -2

2)

`\int\limits^6_2 {f(x)} \, dx =16\\\int\limits^6_2 {g(x)} \, dx =8\\\int\limits^6_2 {(2f(x)-3g(x))} \, dx =2*16-3*8=32-24=6\\\\`