- #1
winston2020
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Homework Statement
Solve the following Integral:
[tex]\int_{1}^2cos(px)dx[/tex]
where p is a constant
Homework Equations
The Attempt at a Solution
I'm totally lost here...
PowerIso said:This isn't to bad. So, let u = px. du = pdx. So can you take it from there?
winston2020 said:So,
[tex]\int_{1}^2cos(px)dx = \int_{1}^2cos(u)\frac{du}{p}[/tex]
[tex]= \frac{sin(u)}{p} + c [/tex]
Is that correct?
The formula for integrating cos(px) is 1/p * sin(px) + C
, where C is the constant of integration.
The process for integrating cos(px) involves using the power rule and the chain rule. First, the power rule is applied to the cos(px)
term, resulting in 1/p * sin(px)
. Then, the chain rule is used to account for the px
term, resulting in a final answer of 1/p * sin(px) + C
.
The limits of integration for integrating cos(px) depend on the specific problem or context in which the integral appears. In general, the limits should be chosen to encompass the entire interval over which the function is being integrated.
The graph of cos(px) does not directly affect the integration process. However, the shape and behavior of the graph may be useful in determining the appropriate limits of integration or in verifying the accuracy of the integrated function.
Integrating cos(px) is a common task in many branches of science and engineering, including physics, mathematics, and signal processing. It can be used to calculate the area under a curve, find the average value of a function, or solve problems involving periodic or oscillatory phenomena.