`y = int_0^(pi/2)3sin(2x)+4cos(x)dx`

Integrating wrt x,

`y = [-3/2cos(2x)+4sin(x)]_0^(pi/2)`

`y = [(-3/2xx(-1)+4xx1)-(-3/2xx1+0)]`

`y = [3/2+3/2+4]`

`y = 7`

Therefore,

`y = int_0^(pi/2)3sin(2x)+4cos(x)dx = 7`

`y = int_0^(pi/2)3sin(2x)+4cos(x)dx`

Integrating wrt x,

`y = [-3/2cos(2x)+4sin(x)]_0^(pi/2)`

`y = [(-3/2xx(-1)+4xx1)-(-3/2xx1+0)]`

`y = [3/2+3/2+4]`

`y = 7`

Therefore,

`y = int_0^(pi/2)3sin(2x)+4cos(x)dx = 7`