∫ 4 cos ( x + 6 π ) cos 2 x ⋅ cos ( 6 5 π + x ) d x

∫ 4 cos ( x + 6 π ) cos 2 x ⋅ cos ( 6 5 π + x ) d x = 2 ∫ ( cos ( 2 x + π ) cos 3 2 π ) cos 2 x d x = 2 ∫ ( − cos 2 x − 2 1 ) cos 2 x d x = ∫ ( − 2 cos 2 2 x − cos 2 x ) d x = − ∫ ( 1 + cos 4 x + cos 2 x ) d x = − x − x sin 4 x − 2 sin 2 x + c

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDefinite Integration by PartsHard2 minPYQ_2010

MathematicsHardsingle choice

$\int 4 cos (x + \frac{π}{6}) cos 2 x \cdot cos (\frac{5 π}{6} + x) d x$

Options:

Answer:

Solution:

$\int 4 cos (x + \frac{π}{6}) cos 2 x \cdot cos (\frac{5 π}{6} + x) d x = 2 \int (cos (2 x + π) cos \frac{2 π}{3}) cos 2 x d x = 2 \int (- cos 2 x - \frac{1}{2}) cos 2 x d x = \int (- 2 cos^{2} 2 x - cos 2 x) d x = - \int (1 + cos 4 x + cos 2 x) d x = - x - \frac{sin 4 x}{x} - \frac{sin 2 x}{2} + c$

Subject:MathematicsTopic:Definite IntegrationSubtopic:Definite Integration by Parts

⏱ 2mℹ️ Source: PYQ_2010

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