   Chapter 8.4, Problem 43E

Chapter
Section
Textbook Problem

# Converting the Limits of Integration In Exercises 37-42, evaluate the definite integral using(a) the given integration limits and (b) the limits obtained by trigonometric substitution. ∫ 0 3 x 3 x 2 + 9 d x

To determine

To calculate: The value of the given definite integral 03x3x2+9dx.

Explanation

Given: The given definite integral is 03x3x2+9dx.

Calculation:

Because (x2+9) is of the form (x2+a2), use the trigonometric substitution x=3tanθdx=3sec2θdθx=03tanθ=0θ=0t=33tanθ3tanθ=1θ=π403x3x2+9dx=0π433tan3θ9tan2θ+93sec2θdθ=0π433tan3θ3secθ3sec2θdθ=0π427tan3

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