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studentxlol
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Homework Statement
If ∫4x dx is read as integrate 4 with respect to x, then what is there's no x so that ∫4 d?. Integrate 4 with respect to nothing?
No, it isn't. It would be read as "integrate 4x with respect to x"studentxlol said:Homework Statement
If ∫4x dx is read as integrate 4 with respect to x,
[itex]\int 4 d[/itex] is an incorrect notation. You do not need an x in the function to be integrated (it can be a constant function) but you cannot have "d" in an integral without a variable: [itex]\int 4dx= 4x+ C[/itex], [itex]\int 4 dt= 4t+ C[/itex], etc.then what is there's no x so that ∫4 d?. Integrate 4 with respect to nothing?
To integrate 4 with no respective variable, you can use the formula for indefinite integrals, which is ∫4 dx = 4x + C, where C is the constant of integration. This means that the integral of 4 with respect to any variable is equal to 4 multiplied by that variable, plus a constant.
Yes, you can solve for the constant of integration by plugging in the given value for the integral into the formula and solving for C. For example, if the integral is equal to 10, then 10 = 4x + C, and you can solve for C by subtracting 4x from both sides.
Yes, it is possible to integrate 4 with no respective variable in definite integrals. In this case, you would need to use the limits of integration to determine the upper and lower bounds of the integral. The formula for definite integrals is ∫a to b 4 dx = 4x |b - 4x |a, where a and b are the limits of integration.
No, the power rule only applies to functions with variables. Since 4 is a constant, it cannot be integrated using the power rule. You would need to use the formula for indefinite integrals or definite integrals, depending on the context of the problem.
Yes, there are other methods for integrating 4 with no respective variable, such as using the substitution method or integration by parts. However, the most straightforward and commonly used method is the formula for indefinite integrals mentioned in the first question.