I think that is an error and so is the integral of tan next to it. I have temporarily hidden them while I get a second opinion. If you look further down the list you will see the same functions again, but this time the correct way round.

Bob

]]>integral of cot(x)= -cosec^2(x)+c

??

Where did that come from?

Bob

ganesh wrote that in his list of formula's just check it once.. you will find my question and i don't think i misunderstood integration for differentiation. if you can show me how is it that we have two formulas for the integration of same function i would appreciate that alot

]]>gourish wrote:

integral of cot(x)= -cosec^2(x)+c

so he was integrating not differentiating.

Bob

]]>then

As far as I can see this is not the same as cot(x). ???

Bob

]]>Where did that come from?

Differentiation.

]]>integral of cot(x)= -cosec^2(x)+c

??

Where did that come from?

Bob

]]>The length of a curve y = f(x) from x = a to x = b is given by

If the curve is represented parametrically by x = f(t) and y = g(t), then the length of the curve from t = a to t = b is given by

In polar coordinates with r = f(θ), the length of the curve from θ = α to θ = β is given by

**Volumes of Revolution**

Disk method:

Washer method:

Shell method:

**Iterated Integrals**

If the double integral of f(x, y) over a region R bounded by f[sub]1[/sub](x) ≤ y ≤ f[sub]2[/sub](x), a ≤ x ≤ b exists, then we may write

This may be extended to triple integrals and beyond.

**Transformations of Multiple Integrals**

If (u, v) are the curvilinear coordinates of a point related to Cartesian coordinates by the transformation equations x = f(u, v), y = g(u, v) which map the region R to R' and G(u, v) = F(f(u, v), g(u, v)) then

This may be extended to triple integrals and beyond.

*Note: See the section on Jacobians in the Partial Differentiation Formulas thread if you do not understand the notation used in "Transformations of Multiple Integrals":*

The integration constant c, to be added on the Right Hand Side, has been omitted.

]]>

If u', u'', u''' etc denote the first, second, third derivatives of the function u and v1, v2, v3 etc are the successive integrals of the function v, then

**Example**

]]>

The integration constant c, to be added on the Right Hand Side, has been omitted.

**Integrals of Inverse Hyperbolic Functions**

The integrand can be rewritten as

or

Let

By solving for A and B, we get A=-5, B=10.

Therefore,

]]>

** Form of the rational function Form of the partial fraction**

where

cannot be factored further.]]>