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Same as any other function - but in the case of a definite integral, you can take advantage of the periodicity. For example, assuming that a certain function has a period of pi, and the value of the definite integral from zero to pi is 2, then the integral from zero to 2 x pi is 4.
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CoachSame as any other function - but in the case of a definite integral, you can take advantage of the periodicity. For example, assuming that a certain function has a period of pi, and the value of the definite integral from zero to pi is 2, then the integral from zero to 2 x pi is 4.
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Which functions has a period?
You can invent any function, to make it periodic. Commonly used functions that are periodic include all the trigonometric functions such as sin and cos (period 2 x pi), tan (period pi). Also, when you work with complex numbers, the exponential function (period 2 x pi x i).
What are periodic functions?
A nonconstant function is called periodic if there exists a number that you can add to (or subtract from) the argument and get the same result. The smallest such positive number is called the period. That is, nonconstant function f(x) is periodic, if and only if f(x) = f(x + h) for some real h. The smallest positive such h is the period. For example, the sine function has period 2*pi, and the function g(x) := [x] - x has period 1.
How do you integrate cot3x dx?
1/3ln(sin3x) + C
Is a function of periodic function periodic?
yes
How do you integrate 2sinxcosx?
Integrate 2sin(x)cos(x)dxLet u = cos(x) and du = -sin(x)dx and pull out the -2:-2[Integral(u*du)]Integrate with respect to u:-2(u2)/2 + CSimplify:-u2 + CReplace u with cos(x):-cos2(x) + C
