Q. 00 - Calculus

Question

Read the section and make your own summary of the material.

Step-by-Step Solution

Answer

Fundamental Theorem of Calculus:

If f is continuous on [a, b] and F is any antiderivative of f , then ${\int }_a^{b}f\left(x\right)dx=F\left(b\right)-F\left(a\right)$.

The Net Change Theorem:

If f is differentiable on [a, b], then .

If the distance travelled in the time t is s(t), then the velocity v(t) is given by, $v\left(t\right)=s\text{'}\left(t\right)$

Step 1. Given Information.

Some definition given in the book.

Step 2. Fundamental Theorem of Calculus.

Fundamental Theorem of Calculus:

If f is continuous on [a, b] and F is any antiderivative of f , then ${\int }_a^{b}f\left(x\right)dx=F\left(b\right)-F\left(a\right)$.

The Net Change Theorem:

If f is differentiable on [a, b], then ${\int }_a^{b}f\text{'}\left(x\right)dx=f\left(b\right)-f\left(a\right)$

If the distance traveled in the time t is s(t), then the velocity v(t) is given by, $v\left(t\right)=s\text{'}\left(t\right)$$v\left(t\right)=s\text{'}\left(t\right)$