# How do you find the definite integral for: #cos(x)# for the intervals #[-pi, pi]#?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the definite integral of cos(x) over the interval [-π, π], you can use the properties of trigonometric functions and integration techniques. The integral of cos(x) from -π to π is equal to the integral of cos(x) from 0 to π plus the integral of cos(x) from -π to 0.

Using the property of evenness of cosine function, the integral of cos(x) from -π to 0 is equal to the integral of cos(x) from 0 to π. Therefore, the definite integral of cos(x) over the interval [-π, π] is twice the integral of cos(x) from 0 to π.

Integrating cos(x) from 0 to π yields sin(x), evaluated from 0 to π. So, sin(π) - sin(0).

Since sin(π) is 0 and sin(0) is 0, the definite integral of cos(x) over the interval [-π, π] is 0.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you evaluate the integral #int x/(x+1)dx# from [0,10]?
- How do you find the sum of the finite geometric sequence of #sum_(j=1)^12 16(1/2)^(j-1)#?
- How do you find the indefinite integral of #int (secxtanx)/(secx-1)#?
- How do you find the integral of #int sqrt(14x-x^2) dx#?
- How do you evaluate #int tan^4xsec^2xdx#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7