- #1
tandoorichicken
- 245
- 0
Ummmm...
If h(x)= -h(-x) for all x, what is [tex] \int_{-a}^{a} h(x) \,dx [/tex]
?
If h(x)= -h(-x) for all x, what is [tex] \int_{-a}^{a} h(x) \,dx [/tex]
?
There's only one possible answer.Originally posted by ShawnD
That question must want a really really generic answer because if it wanted anything specific, you could just make up an answer very easily.
The equation h(x)=-h(-x) means that the function h is an odd function, where the output values for negative inputs are the negative of the output values for positive inputs. This can also be written as h(-x)=-h(x).
To solve h(x)=-h(-x), you can use the property that states the integral of an odd function from -a to a is equal to zero. This means that the area under the curve for positive x values will be equal to the negative of the area under the curve for negative x values.
Solving h(x)=-h(-x) can be useful in finding the area under a curve or the average value of a function over a symmetric interval. It can also help in simplifying integrals and solving differential equations.
Yes, h(x)=-h(-x) can be solved for any value of a since it is a general property of odd functions. However, the specific method of solving may vary depending on the function or interval given.
In addition to finding the area and average value of a function, solving h(x)=-h(-x) can be used in physics and engineering to analyze systems with symmetric properties, such as electric fields or mechanical systems. It can also be applied in signal processing and image analysis.