Learn how to determine the paticular solution with the given condition

The video tutorial explains how to find the function H of X by integrating its derivative, H prime of X. The process involves integrating the expression 8X^3 + 5 to obtain H of X as 2X^4 + 5X + C. The tutorial then demonstrates evaluating H of 1 to solve for the constant C, resulting in the final expression H of X = 2X^4 + 5X - 3.

What is the result of integrating the function 8X^3 + 5?

• 8X^3 + 5X + C

• 2X^3 + 5X + C

• 8X^4 + 5X + C

• 2X^4 + 5X + C

What is the value of H(1) given that H(1) = 4?

• 3

• 1

• 4

• 7

How do you solve for the constant C in the function H(x)?

• By differentiating the function

• By integrating the function

• By substituting a known value into the function

• By graphing the function

What was the mistake corrected in the final function H(x)?

• The constant term was incorrect

• The coefficient of X^4 was incorrect

• The coefficient of X was incorrect

• The function was not integrated properly

What is the final form of the function H(x)?

• 2X^4 + 5X + 3

• 2X^4 + 5X - 3

• 2X^3 + 5X - 3

• 8X^4 + 5X - 3