Integration rules flashcards: core integral methods

Question 1

What does the indefinite integral $\int f(x)\,dx$ represent?

Accepted Answer

The family of antiderivatives of $f$: $$\int f(x)\,dx = F(x)+C,$$ where $F'(x)=f(x)$ and $C$ is an arbitrary constant.

Question 2

When do you use u-substitution?

Accepted Answer

When the integrand contains a composite function and (up to a constant factor) the derivative of the inside function, e.g., $f(g(x))g'(x)$.

Question 3

State the Fundamental Theorem of Calculus (Part 1 and Part 2).

Accepted Answer

FTC 1: If $F(x)=\int_a^x f(t)\,dt$ and $f$ is continuous, then $F'(x)=f(x)$.  FTC 2: If $F'(x)=f(x)$ on $[a,b]$, then $$\int_a^b f(x)\,dx = F(b)-F(a).$$

Integration rules flashcards: core integral methods

Master Math with AI

Learning Resources

Trusted & Recognized