What is the integral of #cos^2[x] sin[x]#?
We want to find:
Remember that the derivative of sine and cosine are basically one another. Since we only have one sine function, it will serve very well as the derivative of the cosine function when we substitute.
Thus:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the integral of ( \cos^2(x) \sin(x) ), you can use the substitution method. Let ( u = \cos(x) ), then ( du = -\sin(x) dx ).
So, the integral becomes:
[ \int \cos^2(x) \sin(x) dx = -\int u^2 du ]
Now, integrate ( -\int u^2 du ):
[ -\int u^2 du = -\frac{u^3}{3} + C ]
Finally, replace ( u ) with ( \cos(x) ):
[ \int \cos^2(x) \sin(x) dx = -\frac{\cos^3(x)}{3} + C ]
Where ( C ) is the constant of integration.
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.
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.

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