Final answer:
The definite integral from 0 to 2 of the function 16 + 7cos(π * x/4) is 34.67.
Step-by-step explanation:
The given question asks for the definite integral from 0 to 2 of the function 16 + 7cos(π * x/4). To find this integral, we can use the integral properties and evaluate the antiderivative of the function within the given limits.
The antiderivative of 16 is 16x, and the antiderivative of 7cos(π * x/4) can be found using the substitution method. Let u = π * x/4, du = π/4 dx. Converting cos(π * x/4) to cos(u) and integrating, we get (4/3)sin(π * x/4).
Now we can evaluate the definite integral. Plugging in the upper limit (2) and lower limit (0) into the antiderivative, the integral evaluates to (16(2) + (4/3)sin(π/2)) - (16(0) + (4/3)sin(0)). Simplifying further, the integral comes out to be 32 + (4/3) = 34.67.