- #1
jra_1574
- 13
- 0
Homework Statement
f:=sin^3(x)cos(y)
Integrate f, from x=y...pi/2)
Homework Equations
I can do it if the two letters were y... But i have no idea how to solve when they are combined..
Last edited:
cristo said:Integrate f with respect to what? Is this a double integration, or a single integration? Please state the question exactly as it is given.
Kreizhn said:In all fairness to jra_1574, I wouldn't say that the question was ambiguous at all. The variable of integration may not have been explicitly stated but the way it was written
"from x=y...Pi/2"
seemed fairly obvious to me, and is in fact the way that some CAS's denote a definite integral (the primary example in mind would be Maple).
As for the actual question jra_1574, the integration doesn't depend on y, and so it's a constant and by linearity can be pulled out of the integral.
Agree with everything you say except for the last line! y is the lower limit of integration and cannot be "pulled out of the integral".
Kreizhn said:In all fairness to jra_1574, I wouldn't say that the question was ambiguous at all. The variable of integration may not have been explicitly stated but the way it was written
"from x=y...Pi/2"
seemed fairly obvious to me
What you mean is that y is a constant when integrating wrt x, and so cos(y) can be treated as a constant.As for the actual question jra_1574, the integration doesn't depend on y, and so it's a constant and by linearity can be pulled out of the integral.
Since cos(y) is a constant (with respect to x) it can be "pulled out of the integral". That is different from saying y (which is also the lower limit of integration) can be "pulled out of the integral".Office_Shredder said:What if instead it was written as f=sin(x)^3cos(0) and was integrated from 0 to pi/2. Couldn't the cos(0) be pulled out of the integral? I'm not sure how this is supposed to be any different
The integration of f from x=y to pi/2 represents the area under the curve of the function f, bounded by the lines x=y and x=pi/2.
The process for solving this type of integral involves using integration techniques such as substitution, integration by parts, or partial fractions to simplify the integrand. Then, the integrand is integrated with respect to the variable of integration, typically using the fundamental theorem of calculus.
It depends on the function f. Some integrals can be solved analytically using known integration techniques, while others may require numerical methods for approximation.
The bounds of an integral represent the limits of integration, in this case, x=y and x=pi/2 represent the starting and ending points for the integration process. These bounds define the region over which the integral is being evaluated.
The purpose of solving an integral is to find the exact value of the area under a curve, which can have real-world applications in fields such as physics, engineering, economics, and more. Integrals are also used to find the antiderivative of a function.