Having trouble finding error bound due to an undefined term

Question

I need to find the error in the approximation of this integral ussign the midpoint rule. $$\int^4_0e^{\sqrt{x}} \sin x\, dx$$ The error is given by the equation $$|E|\leq\dfrac{K_2(b-a)^3}{24n^2}$$Where $K_2$ is the upper bound of the second derivative of the function. Problem is the second derivative of the functon is unbounded there is no maximum value, how can I solve this problem ?

Answer 1

$K_2$ is the bound on the second derivative on the interval of integration. Sure, it's h bounded in $\mathbb{R}$ but it's not unbounded on $[0,4]$.