# Write a definite integral that yields the area of the region. (Do not evaluate the integral.)?

Based on the properties of the integrals we therefore know that

We can also easily evaluate the integral using additivity:

Substitute in the second integral:

So:

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 find the volume of the solid that lies within the sphere #x^2+y^2+z^2 =25#, above the xy plane, and outside the cone?
- Let R be the region in the first quadrant enclosed by the graphs of #y=e^(-x^2)#, #y=1-cosx#, and the y axis, how do you find the volume of the solid generated when the region R is revolved about the x axis?
- How do you find the volume of the parallelepiped determined by the vectors: <1,3,7>, <2,1,5> and <3,1,1>?
- How do you find the area between the curves #x+3y=21# and #x+7=y^2#?
- The region under the curves #y=sinx/x, pi/2<=x<=pi# is rotated about the x axis. How do you find the volumes of the two solids of revolution?

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