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Chapter 4: Q. 1 (page 402)

Consider the differential equation f'(x)=g(x). What has to be true about g(x)for the Second Fundamental Theorem of Calculus to guarantee that a function fexists that satisfies f'(x)=g(x)?

Short Answer

Expert verified

For, f'(x)=g(x)to be true two conditions need to be satisfied:

Fis continuous on a,band differentiable on a,b.

Fis an antiderivative of f, that is,F'(x)=f(x).

Step by step solution

01

Step 1. Given Information.

The objective to be true is to explain the second fundamental theorem of calculus.

02

Step 2. The conditions.

For, f'(x)=g(x)to be true two conditions need to be satisfied:

Fis continuous on a,band differentiable on a,b.

Fis an antiderivative offthat is, F'(x)=f(x).

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