Evaluate the integral with the square root using u substitution

The video tutorial explains the process of using U substitution in integration. It begins by defining U as X + 7 and solving for X. The instructor then sets up the integral using U substitution, ensuring all terms are correctly represented. The integration is performed using the power rule, and the solution is simplified. Finally, the instructor makes adjustments to the solution and plugs back the original variable to complete the process.

What is the initial substitution made for U in terms of X?

• U = X - 5

• U = X - 7

• U = X + 7

• U = X + 5

How is the extra X in the equation handled during substitution?

• By ignoring it

• By solving for X in terms of U

• By adding it to U

• By multiplying it with U

What is U to the 1/2 power equivalent to?

• sqrt(X + 7)

• X + 7

• U + 7

• sqrt(U + 7)

Which rule is used to integrate the expression after substitution?

• Chain Rule

• Quotient Rule

• Power Rule

• Product Rule

What is the final step after integrating the expression?

• Simplifying the expression

• Adding a constant C

• Substituting back the original variable X

• Differentiating the result