   Chapter 4.4, Problem 35E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 1 8 2 + t t 2 3 d t

To determine

To evaluate:

182+tt23dt

Explanation

1) Concept:

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

The fundamental theorem of calculus:

If f is continuous on [a, b], then abfxdx=Fb-F(a) where F is the anti derivative of f.

2) Formula:

fx+gxdx=fxdx+gxdx

xndx=xn+1n+1+C

kdx=kx+C

3) Given:

182+tt23dt

4) Calculation:

Consider, 182+tt23dt

By using the rules of exponent,

182+tt23dt= 182t-23+t13dt

Applying the rules of integral:

After separating the integrals,

18t-23+t13dt=182t-23dt+1

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