A) State the chain rule for integration
Ans. The chain rule for integration is also known as " Integration by substitution "
Integration by substitution is taken in order to make integration solve easily in few steps.
For,
Instead of expanding term
With substitution of and
We simplified the integration as
By replacaing value of u=x+2
B) State the rule of differentiation for the sine function.
Ans. We know that
C) Find the indefinite integral using substitution.
Ans.
Given,
Take y = Sin14x
Differentiating both side
Substituting values in integration,
Replacing values in the integration
D)Check your work by taking a derivative of your answer from part C.
Ans.
Answer for Part C is
Differentiating the answer
we get,