6.2 Constructing Antiderivatives Analytically

Question 1

What does constructing antiderivatives analytically mean?

Answer 1

figuring out which function, when differentiated, gives you the given function

Question 1

What is the most basic rule for finding an antiderivative and how does it work?

Answer 1

The power rule: If f(x)=x^n
,the antiderivative is F(x)= x(n+1)/n+1+C where C is a constant.

Question 2

What is the antiderivative of a constant
k?

Answer 2

F(x)=kx+C, where C is a constant.

Question 3

What is the antiderivative of e^(x)?

Answer 3

The antiderivative of e^(x)
+C, where C is a constant.

Question 4

What is a tip to handle more complex functions like sums or differences?

Answer 4

Find the antiderivative of each part separately, then add or subtract them.

Question 5

What is the constant of integration
C and why?

Answer 5

C represents any constant that could be added because when you take the derivative of a constant, it becomes zero.