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elabed haidar
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Homework Statement
simple question what is the integral of sinx/x i really tried but i couldn't find the trick
The formula for integrating sinx/x is ∫sindx = -cosx + C. This is known as the antiderivative of sinx, which is the function that when differentiated gives sinx.
Integrating sinx/x is a common homework question because it involves using one of the fundamental integration formulas and requires applying certain techniques and rules, making it a good practice for students learning integration.
To solve an integral with sinx/x, you can use the formula ∫sindx = -cosx + C and integrate the function directly. However, if the integral is more complex, you may need to employ substitution or integration by parts to solve it.
Yes, in addition to the formula ∫sindx = -cosx + C, you can also use trigonometric identities such as sin2x = 2sinxcosx or sin^2x = (1-cos2x)/2 to simplify the integral and make it easier to integrate.
Yes, there are special cases when integrating sinx/x. For example, if the integral is evaluated at 0, the result would be undefined since the function is not defined at x=0. Also, if the integral is evaluated at ∞, the result would be π/2.