10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

Finding or Evaluating an Integral In Exercises 55–62, find or evaluate the integral.

∫ 0 π / 2 1 3 − 2 cos θ d θ

To determine

To calculate: The value of the definite integral ∫0π/213−2cosθdθ by the use of a table of integrals.

The integral is: ∫0π/213−2cosθdθ.

Formula used:

Use the formula 23 from the table of integrals:

∫1a2+u2du=1aarctanua+C

Calculation:

Consider the provided integral,

∫0π/213−2cosθdθ

Let u=tanθ2. Then du=2sec2θ2dθ.

sinθ=2u1+u2sec2θ2=11+u2

Now, substitute the values in the provided integral. Then,

∫0π/213−2cosθdθ=∫012du1+u23−2(1−u2)1+

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Finding or Evaluating an Integral In Exercises 55–62, find or evaluate the integral.

∫ 0 π / 2 1 3 − 2 cos θ d θ

Chapter 8 Solutions

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Calculus

Finding or Evaluating an Integral In Exercises 55–62, find or evaluate the integral. ∫ 0 π / 2 1 3 − 2 cos θ d θ

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Calculus Calculus 10th Edition

Finding or Evaluating an Integral In Exercises 55–62, find or evaluate the integral.

∫ 0 π / 2 1 3 − 2 cos θ d θ