- #1
frozen7
- 163
- 0
Integrate (x^2 / sinx) / (1 + x^6):
How to do this? I just need some clues...
How to do this? I just need some clues...
frozen7 said:and from x = - pi / 2 to x = pi / 2
frozen7 said:Erm...may I know what is odd and even function?
It IS a proper way!frozen7 said:Ya. Thanks. Finally i catch the ball. But how should I answer this question in a proper way? Is there any other answering method for this question?
There's a little proof:frozen7 said:Ya. Thanks. Finally i catch the ball. But how should I answer this question in a proper way? Is there any other answering method for this question?
frozen7 said:By plotting the graph of sinx , the area within [tex]\frac{-\Pi}{2}[/tex] and [tex]\frac{\Pi}{2}[/tex] is zero and also know that the function is an odd function. So, what I get is only the value of sinx , how about [tex]\frac{x^2}{1+x^6}[/tex]?
Okay, you should look back at your text-book. There should be a part that states:frozen7 said:how come [tex]\int \limits_{0} ^ \alpha f(-u) du = \int \limits_{0} ^ \alpha f(u) du = \int \limits_{0} ^ \alpha f(x) dx[/tex]
Shouldn`t it be [tex]\int \limits_{0} ^ \alpha f(-u) du = \int \limits_{0} ^ \alpha f(u) du = \int \limits_{0} ^ {-\alpha} f(x) dx[/tex]
The formula for integrating (x^2 / sinx) / (1 + x^6) is ∫ (x^2 / sinx) / (1 + x^6) dx = 1/3ln(1 + x^6) + C, where C is the constant of integration.
Yes, the integral can be solved using the substitution u = 1 + x^6. This will result in the integral becoming ∫ (x^2 / sinx) / u du, which can then be solved using integration by parts.
The possible methods for solving the integral (x^2 / sinx) / (1 + x^6) include substitution, integration by parts, and partial fraction decomposition.
Yes, it is possible to solve the integral (x^2 / sinx) / (1 + x^6) using a computer program or calculator. However, the result may be in terms of an antiderivative and not a definite integral, unless specific limits of integration are provided.
Yes, the integral (x^2 / sinx) / (1 + x^6) may have special cases or restrictions depending on the limits of integration. For example, if the limits include values where sinx = 0 or x = ±√(1 + x^6), the integral may not be solvable using traditional methods.