- #1
iRaid
- 559
- 8
Homework Statement
[itex]\int cos^{2}x dx[/itex]
I know that
[itex]cos^{2}x = \frac{1+cos2x}{2}[/itex]
but I don't see how that helps me.
Can someone help walk me through it..
iRaid said:u=2x du=(1/2)dx
(1/2)∫cosudu
=(1/4)sin2x
So then..
x/2 + (1/4)sin2x
but that's not the answer..
Dick said:I think it is the correct answer. You should probably put a +C on it. Is that the problem?
The integral of cos^2(x) is (1/2)x + (1/4)sin(2x) + C. This can be derived using integration by parts or by using the trigonometric identity cos^2(x) = (1/2)(1 + cos(2x)).
To solve an integral with cos^2(x), you can use integration by parts or the trigonometric identity cos^2(x) = (1/2)(1 + cos(2x)) to simplify the integral. Then, you can use basic integration techniques such as substitution or integration by parts to find the solution.
Yes, most scientific calculators have the ability to solve integrals. However, it is important to understand the steps involved in solving the integral by hand in order to use the calculator correctly.
The limits of integration for a cos^2(x) integral will depend on the specific problem you are trying to solve. They can be given in the problem or you may need to determine them by looking at the graph of the function.
Yes, there are special cases when solving a cos^2(x) integral. For example, if the limits of integration are from 0 to π/2, the integral simplifies to π/4. Additionally, if the limits of integration are from 0 to π, the integral simplifies to π/2. It is important to be aware of these special cases when solving cos^2(x) integrals.