   Chapter 4.R, Problem 12E

Chapter
Section
Textbook Problem

# Evaluate the integral, if it exists. ∫ 0 T ( x 4 − 8 x + 7 )   d x

To determine

To evaluate:

0T(x4-8x+7)dx if it exists

Explanation

1) Concept:

By using fundamental theorem of calculus and rules of integration evaluate the given integral.

2) Theorem:

Fundamental theorem of calculus:

If f is continuous on [a, b], then abfxdx=Fb-Fa.

3) Formula:

xndx=xn+1n+1+C

3) Given:

0T(x4-8x+7)dx

4) Calculation:

Consider, 0T(x4-8x+7)dx

Since the function is continuous on real numbers, the integral exists for all T

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