Integration of Circular Functions (VCE SSCE Mathematical Methods): Flashcards

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Integration of circular functions
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sin(kx+a)dx\int \sin(kx + a) dx equals

1kcos(kx+a)+c-\frac{1}{k}\cos(kx + a) + c

cos(kx+a)dx\int \cos(kx + a) dx equals

1ksin(kx+a)+c\frac{1}{k}\sin(kx + a) + c

Meaning of kk in sin(kx+a)\sin(kx + a)

Frequency of the circular function

Meaning of aa in sin(kx+a)\sin(kx + a)

Phase shift (horizontal translation)

Why divide by kk when integrating circular functions

Chain rule working in reverse

Why negative sign when integrating sine

Derivative of cosine is negative sine

Meaning of cc in indefinite integrals

Constant of integration

Finding area when curve below x-axis

Take negative of integral or split integral

Handling constant factors in integrals

Take outside the integral

Values for definite integrals of circular functions

Exact values for common angles (π4\frac{\pi}{4}, π2\frac{\pi}{2}, etc.)

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