Math Problem Statement
Evaluate the following integral using integration by parts. Integral from nothing to nothing x sine one seventh x dx Question content area bottom Part 1 Use the integration by parts formula so that the new integral is simpler than the original one. Choose the correct answer below. A.negative 7 cosine one seventh x minus Integral from nothing to nothing left parenthesis negative 7 x cosine one seventh x right parenthesis dx negative 7 cosine one seventh x minus Integral from nothing to nothing left parenthesis negative 7 x cosine one seventh x right parenthesis dx B.one seventh x cosine 7 x plus Integral from nothing to nothing left parenthesis one seventh cosine 7 x right parenthesis dx one seventh x cosine 7 x plus Integral from nothing to nothing left parenthesis one seventh cosine 7 x right parenthesis dx C.7 x cosine one seventh x plus Integral from nothing to nothing left parenthesis 7 cosine one seventh x right parenthesis dx 7 x cosine one seventh x plus Integral from nothing to nothing left parenthesis 7 cosine one seventh x right parenthesis dx D.negative 7 x cosine one seventh x minus Integral from nothing to nothing left parenthesis negative 7 cosine one seventh x right parenthesis dx negative 7 x cosine one seventh x minus Integral from nothing to nothing left parenthesis negative 7 cosine one seventh x right parenthesis dx Part 2 Evaluate the integral.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Integration by Parts
Trigonometric Functions
Formulas
Integration by Parts formula: ∫u dv = uv - ∫v du
Trigonometric integrals: ∫sin(ax) dx = -1/a cos(ax), ∫cos(ax) dx = 1/a sin(ax)
Theorems
Integration by Parts Theorem
Chain Rule for Integration
Suitable Grade Level
Grades 11-12 or early college level