Applying linearity to evaluate a definite integral

By linearity of the definite integral, we can split the sum and pull out the constant factor: $\int_{-3}^{3}\left[5f(x)+7\right]dx = 5\int_{-3}^{3}f(x)\,dx + \int_{-3}^{3}7\,dx.$ We are told $\int_{-3}^{3}f(x)\,dx = 0$, so the first term becomes $5(0) = 0$.

For the second term, the integral of the constant function $7$ over $[-3,3]$ equals $7$ times the length of the interval: $\int_{-3}^{3}7\,dx = 7(3-(-3)) = 7(6) = 42$. Adding the two results gives $0 + 42 = 42$.

Yes, the answer would double. Since the odd function part still contributes zero, the entire result comes from the constant term, which scales linearly with the constant's value. Doubling the constant from seven to fourteen doubles that term from forty-two to eighty-four. So the final answer would become eighty-four instead of forty-two.