7 ### Maximizing the Integral Value for FunctionsIn this exercise, you are tasked with finding two numbers \( a \) and \( b \) with the condition \( a \leq b \) such that the following integral is maximized:\[\int_{a}^{b} (6 - 5x - x^2)^{1/3} \, dx\]To approach this problem:1. **Understand the Function**: The integrand \((6 - 5x - x^2)^{1/3}\) is a function you will integrate over the interval \([a, b]\). 2. **Determine \( a \) and \( b \)**: You need to find the limits of the integral, \( a \) and \( b \), that will result in the largest possible value of the integral.3. **Maximization Strategy**: Utilize calculus techniques, such as finding critical points and examining the intervals for maximum values, to determine the optimal \( a \) and \( b \).#### Input Fields- **a =** [Input Box] : Enter the value of \( a \) here.- **b =** [Input Box] : Enter the value of \( b \) here.By solving this problem, you will practice optimization in the context of definite integrals, a key concept in calculus.

Name: 7 ### Maximizing the Integral Value for FunctionsIn this exercise, you
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 7 ### Maximizing the Integral Value for FunctionsIn this exercise, you are tasked with finding two numbers \( a \) and \( b \) with the condition \( a \leq b \) such that the following integral is maximized:\[\int_{a}^{b} (6 - 5x - x^2)^{1/3} \, dx\]