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MATH 2B Lecture 12: 7.3 Trigonometric Substitution

United States

Single-Variable Calculus

Mathematics

Gholamhossien Erjaee

University of California - Irvine

Introduction to Ecology

Problems in History: Europe

Boolean Algebra and Logic

Introduction to International Relations

Introduction to Sociology

Trigonometric Substitution: Make the indicated trigonometric substitution in the given algebraic expression simplify. Assume that <img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="0%3Ctheta%3C%5Cfrac%7Bpi%7D%7B2%7D"><img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="%5Cfrac%7Bx%7D%7B%5Csqrt%7B1-x%5E%7B2%7D%7D%7D%2Cx%3Dsintheta">

Trigonometric Substitution: Make the indicated trigonometric substitution in the given algebraic expression simplify. Assume that <img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="0%3Ctheta%3C%5Cfrac%7Bpi%7D%7B2%7D"><img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="%5Csqrt%7B1%2Bx%5E%7B2%7D%7D%2Cx%3Dtantheta">

Trigonometric Substitution: Make the indicated trigonometric substitution in the given algebraic expression simplify. Assume that <img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="0%3Ctheta%3C%5Cfrac%7Bpi%7D%7B2%7D"><img src="data:image/png;base64,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" class="fm-editor-equation" data-mlang="latex" data-equation="%5Csqrt%7Bx%5E%7B2%7D-1%7D%2Cx%3Dsectheta">

MATH 2B Lecture 12: 7.3 Trigonometric Substitution

MATH 2B Full Course Notes

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