Grade 12Integral Calculus
Integrate x sin(2x) dx
Integrate x sin(2x) dx
2 Answers
grenade
Approved Tutor Answer11 Years agoIntegrate the original integrand by parts:
∫ xsin(2x) dx
Let f'(x) = sin(2x)
f(x) = -cos(2x) / 2
Let g(x) = x
g'(x) = 1
∫ f'(x)g(x) dx = f(x)g(x) - ∫ f(x)g'(x) dx
∫ xsin(2x) dx = -xcos(2x) / 2 + ∫ cos(2x) / 2 dx
∫ xsin(2x) dx = -xcos(2x) / 2 + sin(2x) / 4 + C
∫ xsin(2x) dx = sin(2x) / 4 - xcos(2x) / 2 + C
∫ xsin(2x) dx
Let f'(x) = sin(2x)
f(x) = -cos(2x) / 2
Let g(x) = x
g'(x) = 1
∫ f'(x)g(x) dx = f(x)g(x) - ∫ f(x)g'(x) dx
∫ xsin(2x) dx = -xcos(2x) / 2 + ∫ cos(2x) / 2 dx
∫ xsin(2x) dx = -xcos(2x) / 2 + sin(2x) / 4 + C
∫ xsin(2x) dx = sin(2x) / 4 - xcos(2x) / 2 + C
aiu
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