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Integrate the function (3-5x)cos4x.SolutionOne of the techniq.pdf

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Integrate the function (3-5x)*cos4x. Solution One of the techniques for evaluating integrals is integration by parts. We\'ll express the formula of integration by parts using differentials: Int u dv = u*v - Int v du We\'ll put u = 3 - 5x We\'ll differentiate both sides: du = -5dx We\'ll put dv = cos(4x) dx. We\'ll integrate both sides: Int dv = Int cos(4x) dx v = (sin 4x)/4 We\'ll substitute in the formula of integral: Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 + 5 Int (sin 4x)dx/4 Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 + (5/4)Int (sin 4x)dx Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 + (5/4)[(1/4)(- cos 4x)] + C Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 - (5/16)[(cos 4x)] + C.

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Integrate the function (3-5x)*cos4x. Solution One of the techniques for evaluating integrals is integration by parts. We'll express the formula of integration by parts using differentials: Int u dv = u*v - Int v du We'll put u = 3 - 5x We'll differentiate both sides: du = -5dx We'll put dv = cos(4x) dx. We'll integrate both sides: Int dv = Int cos(4x) dx v = (sin 4x)/4 We'll substitute in the formula of integral: Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 + 5 Int (sin 4x)dx/4 Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 + (5/4)Int (sin 4x)dx Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 + (5/4)[(1/4)(- cos 4x)] + C Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 - (5/16)[(cos 4x)] + C

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Integrate the function (3-5x)cos4x.SolutionOne of the techniq.pdf

  • 1. Integrate the function (3-5x)*cos4x. Solution One of the techniques for evaluating integrals is integration by parts. We'll express the formula of integration by parts using differentials: Int u dv = u*v - Int v du We'll put u = 3 - 5x We'll differentiate both sides: du = -5dx We'll put dv = cos(4x) dx. We'll integrate both sides: Int dv = Int cos(4x) dx v = (sin 4x)/4 We'll substitute in the formula of integral: Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 + 5 Int (sin 4x)dx/4 Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 + (5/4)Int (sin 4x)dx Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 + (5/4)[(1/4)(- cos 4x)] + C Int (3 - 5x) cos(4x) dx = (3 - 5x)*(sin 4x)/4 - (5/16)[(cos 4x)] + C