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Chapter 4: Q. 00 (page 372)

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Short Answer

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Fundamental Theorem of Calculus:

If f is continuous on[a, b] and F is any antiderivative of f , then ∫abf(x)dx=F(b)-F(a).

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(t)=s'(t)

Step by step solution

01

Step 1. Given Information.

Some definition given in the book.

02

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 ∫abf(x)dx=F(b)-F(a).

The Net Change Theorem:

If f is differentiable on [a, b], then ∫abf'(x)dx=f(b)-f(a)

If the distance traveled in the time t is s(t), then the velocity v(t) is given by, v(t)=s'(t)v(t)=s'(t)

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