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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 8, Problem 114RE
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Evaluating a Definite Integral In Exercises 111-118, evaluate the definite integral.

∫ − π π 1 2 ( 1 + cos   2 x ) d x

To determine

To calculate: The value of definite integral ∫−ππ12(1+cos2x)dx.

Explanation

Given Information:

The provided integral is ∫−ππ12(1+cos2x)dx.

Formula used:

Write the formula of definite integral of ∫abcosnudu as,

∫abcosnudu=[sinnun]ab

Here, n is the any integer.

Write the formula of definite integral of ∫abdu.

∫abdu=[u]ab

Calculation:

The provided integral is,

∫−ππ12(1+cos2x)dx

Rewrite.

∫−ππ12(1+cos2x)dx=12[∫−ππdx+∫−ππcos2xdx]

Integrate with the help of above integration formulae

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Sect-8.1 P-1CPSect-8.1 P-2CPSect-8.1 P-3CPSect-8.1 P-4CPSect-8.1 P-1SWUSect-8.1 P-2SWUSect-8.1 P-3SWUSect-8.1 P-4SWUSect-8.1 P-5SWUSect-8.1 P-6SWU
Sect-8.1 P-7SWUSect-8.1 P-8SWUSect-8.1 P-9SWUSect-8.1 P-10SWUSect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10ESect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-31ESect-8.1 P-32ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.1 P-47ESect-8.1 P-48ESect-8.1 P-49ESect-8.1 P-50ESect-8.1 P-51ESect-8.1 P-52ESect-8.1 P-53ESect-8.1 P-54ESect-8.1 P-55ESect-8.1 P-56ESect-8.1 P-57ESect-8.1 P-58ESect-8.2 P-1CPSect-8.2 P-2CPSect-8.2 P-3CPSect-8.2 P-4CPSect-8.2 P-5CPSect-8.2 P-6CPSect-8.2 P-7CPSect-8.2 P-1SWUSect-8.2 P-2SWUSect-8.2 P-3SWUSect-8.2 P-4SWUSect-8.2 P-5SWUSect-8.2 P-6SWUSect-8.2 P-7SWUSect-8.2 P-8SWUSect-8.2 P-9SWUSect-8.2 P-10SWUSect-8.2 P-11SWUSect-8.2 P-12SWUSect-8.2 P-1ESect-8.2 P-2ESect-8.2 P-3ESect-8.2 P-4ESect-8.2 P-5ESect-8.2 P-6ESect-8.2 P-7ESect-8.2 P-8ESect-8.2 P-9ESect-8.2 P-10ESect-8.2 P-11ESect-8.2 P-12ESect-8.2 P-13ESect-8.2 P-14ESect-8.2 P-15ESect-8.2 P-16ESect-8.2 P-17ESect-8.2 P-18ESect-8.2 P-19ESect-8.2 P-20ESect-8.2 P-21ESect-8.2 P-22ESect-8.2 P-23ESect-8.2 P-24ESect-8.2 P-25ESect-8.2 P-26ESect-8.2 P-27ESect-8.2 P-28ESect-8.2 P-29ESect-8.2 P-30ESect-8.2 P-31ESect-8.2 P-32ESect-8.2 P-33ESect-8.2 P-34ESect-8.2 P-35ESect-8.2 P-36ESect-8.2 P-37ESect-8.2 P-38ESect-8.2 P-39ESect-8.2 P-40ESect-8.2 P-41ESect-8.2 P-42ESect-8.2 P-43ESect-8.2 P-44ESect-8.2 P-45ESect-8.2 P-46ESect-8.2 P-47ESect-8.2 P-48ESect-8.2 P-49ESect-8.2 P-50ESect-8.2 P-51ESect-8.2 P-52ESect-8.2 P-53ESect-8.2 P-54ESect-8.2 P-55ESect-8.2 P-56ESect-8.2 P-57ESect-8.2 P-58ESect-8.2 P-59ESect-8.2 P-60ESect-8.2 P-61ESect-8.2 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P-20ESect-8.3 P-21ESect-8.3 P-22ESect-8.3 P-23ESect-8.3 P-24ESect-8.3 P-25ESect-8.3 P-26ESect-8.3 P-27ESect-8.3 P-28ESect-8.3 P-29ESect-8.3 P-30ESect-8.3 P-31ESect-8.3 P-32ESect-8.3 P-33ESect-8.3 P-34ESect-8.3 P-35ESect-8.3 P-36ESect-8.3 P-37ESect-8.3 P-38ESect-8.3 P-39ESect-8.3 P-40ESect-8.3 P-41ESect-8.3 P-42ESect-8.3 P-43ESect-8.3 P-44ESect-8.3 P-45ESect-8.3 P-46ESect-8.3 P-47ESect-8.3 P-48ESect-8.3 P-49ESect-8.3 P-50ESect-8.3 P-51ESect-8.3 P-52ESect-8.3 P-53ESect-8.3 P-54ESect-8.3 P-55ESect-8.3 P-56ESect-8.3 P-57ESect-8.3 P-58ESect-8.3 P-59ESect-8.3 P-60ESect-8.3 P-61ESect-8.3 P-62ESect-8.3 P-63ESect-8.3 P-64ESect-8.3 P-65ESect-8.3 P-66ESect-8.3 P-67ESect-8.3 P-68ESect-8.3 P-69ESect-8.3 P-70ESect-8.3 P-71ESect-8.3 P-72ESect-8.3 P-73ESect-8.3 P-74ESect-8.3 P-75ESect-8.3 P-76ESect-8.3 P-77ESect-8.3 P-78ESect-8.3 P-79ESect-8.3 P-80ESect-8.3 P-81ESect-8.3 P-82ESect-8.3 P-83ESect-8.3 P-84ESect-8.3 P-85ESect-8.3 P-86ESect-8.3 P-87ESect-8.3 P-88ESect-8.3 P-1QYSect-8.3 P-2QYSect-8.3 P-3QYSect-8.3 P-4QYSect-8.3 P-5QYSect-8.3 P-6QYSect-8.3 P-7QYSect-8.3 P-8QYSect-8.3 P-9QYSect-8.3 P-10QYSect-8.3 P-11QYSect-8.3 P-12QYSect-8.3 P-13QYSect-8.3 P-14QYSect-8.3 P-15QYSect-8.3 P-16QYSect-8.3 P-17QYSect-8.3 P-18QYSect-8.3 P-19QYSect-8.3 P-20QYSect-8.3 P-21QYSect-8.3 P-22QYSect-8.3 P-23QYSect-8.3 P-24QYSect-8.3 P-25QYSect-8.4 P-1CPSect-8.4 P-2CPSect-8.4 P-3CPSect-8.4 P-4CPSect-8.4 P-5CPSect-8.4 P-6CPSect-8.4 P-7CPSect-8.4 P-8CPSect-8.4 P-9CPSect-8.4 P-1SWUSect-8.4 P-2SWUSect-8.4 P-3SWUSect-8.4 P-4SWUSect-8.4 P-5SWUSect-8.4 P-6SWUSect-8.4 P-7SWUSect-8.4 P-8SWUSect-8.4 P-9SWUSect-8.4 P-10SWUSect-8.4 P-1ESect-8.4 P-2ESect-8.4 P-3ESect-8.4 P-4ESect-8.4 P-5ESect-8.4 P-6ESect-8.4 P-7ESect-8.4 P-8ESect-8.4 P-9ESect-8.4 P-10ESect-8.4 P-11ESect-8.4 P-12ESect-8.4 P-13ESect-8.4 P-14ESect-8.4 P-15ESect-8.4 P-16ESect-8.4 P-17ESect-8.4 P-18ESect-8.4 P-19ESect-8.4 P-20ESect-8.4 P-21ESect-8.4 P-22ESect-8.4 P-23ESect-8.4 P-24ESect-8.4 P-25ESect-8.4 P-26ESect-8.4 P-27ESect-8.4 P-28ESect-8.4 P-29ESect-8.4 P-30ESect-8.4 P-31ESect-8.4 P-32ESect-8.4 P-33ESect-8.4 P-34ESect-8.4 P-35ESect-8.4 P-36ESect-8.4 P-37ESect-8.4 P-38ESect-8.4 P-39ESect-8.4 P-40ESect-8.4 P-41ESect-8.4 P-42ESect-8.4 P-43ESect-8.4 P-44ESect-8.4 P-45ESect-8.4 P-46ESect-8.4 P-47ESect-8.4 P-48ESect-8.4 P-49ESect-8.4 P-50ESect-8.4 P-51ESect-8.4 P-52ESect-8.4 P-53ESect-8.4 P-54ESect-8.4 P-55ESect-8.4 P-56ESect-8.4 P-57ESect-8.4 P-58ESect-8.4 P-59ESect-8.4 P-60ESect-8.4 P-61ESect-8.4 P-62ESect-8.4 P-63ESect-8.4 P-64ESect-8.4 P-65ESect-8.4 P-66ESect-8.4 P-67ESect-8.4 P-68ESect-8.4 P-69ESect-8.4 P-70ESect-8.4 P-71ESect-8.4 P-72ESect-8.4 P-73ESect-8.4 P-74ESect-8.4 P-75ESect-8.4 P-76ESect-8.4 P-77ESect-8.4 P-78ESect-8.4 P-79ESect-8.4 P-80ESect-8.4 P-81ESect-8.4 P-82ESect-8.4 P-83ESect-8.4 P-84ESect-8.5 P-1CPSect-8.5 P-2CPSect-8.5 P-3CPSect-8.5 P-4CPSect-8.5 P-5CPSect-8.5 P-6CPSect-8.5 P-7CPSect-8.5 P-8CPSect-8.5 P-9CPSect-8.5 P-1SWUSect-8.5 P-2SWUSect-8.5 P-3SWUSect-8.5 P-4SWUSect-8.5 P-5SWUSect-8.5 P-6SWUSect-8.5 P-7SWUSect-8.5 P-8SWUSect-8.5 P-9SWUSect-8.5 P-10SWUSect-8.5 P-11SWUSect-8.5 P-12SWUSect-8.5 P-13SWUSect-8.5 P-14SWUSect-8.5 P-15SWUSect-8.5 P-16SWUSect-8.5 P-17SWUSect-8.5 P-18SWUSect-8.5 P-19SWUSect-8.5 P-20SWUSect-8.5 P-1ESect-8.5 P-2ESect-8.5 P-3ESect-8.5 P-4ESect-8.5 P-5ESect-8.5 P-6ESect-8.5 P-7ESect-8.5 P-8ESect-8.5 P-9ESect-8.5 P-10ESect-8.5 P-11ESect-8.5 P-12ESect-8.5 P-13ESect-8.5 P-14ESect-8.5 P-15ESect-8.5 P-16ESect-8.5 P-17ESect-8.5 P-18ESect-8.5 P-19ESect-8.5 P-20ESect-8.5 P-21ESect-8.5 P-22ESect-8.5 P-23ESect-8.5 P-24ESect-8.5 P-25ESect-8.5 P-26ESect-8.5 P-27ESect-8.5 P-28ESect-8.5 P-29ESect-8.5 P-30ESect-8.5 P-31ESect-8.5 P-32ESect-8.5 P-33ESect-8.5 P-34ESect-8.5 P-35ESect-8.5 P-36ESect-8.5 P-37ESect-8.5 P-38ESect-8.5 P-39ESect-8.5 P-40ESect-8.5 P-41ESect-8.5 P-42ESect-8.5 P-43ESect-8.5 P-44ESect-8.5 P-45ESect-8.5 P-46ESect-8.5 P-47ESect-8.5 P-48ESect-8.5 P-49ESect-8.5 P-50ESect-8.5 P-51ESect-8.5 P-52ESect-8.5 P-53ESect-8.5 P-54ESect-8.5 P-55ESect-8.5 P-56ESect-8.5 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