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KAS90
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hi there.. I want to know how to integrate inverse trigonometric functions?like inverse tanx for example?
thanx a lot..I just want a brief explanation?
thanx a lot..I just want a brief explanation?
KAS90 said:hi there.. I want to know how to integrate inverse trigonometric functions?like inverse tanx for example?
thanx a lot..I just want a brief explanation?
tiny-tim said:Hi KAS90! Welcome to PF!
You want dy/dx for y = tan-1x.
So rewrite it x = tany, dx = sec2y dy
so dy/dx = cos2y
and then convert that back to a function of x.
Same method for any inverse fucnction!
d_leet said:I think the OP wanted to integrate, not differentiate. In that case may I suggest integration by parts.
KAS90 said:the integration of xtan-1x will be solved using integration by parts.. the question is:
u=x
du=dx
dv=tan-1x dx
v=?
or shall i solve it the other way round..
u=tan-1x dx
dv=xdx?
I mean, is there really a definite integral for inverse trig functions?
Thanx again 2 u, da_vinci,d_leet...
An inverse function is a function that undoes the original function's actions, essentially reversing the input and output relationship. For example, if f(x) = 2x, the inverse function would be f-1(x) = x/2.
To find the inverse of a function, switch the x and y variables and solve for y. This will give you the inverse function in terms of x. It is also important to check that the inverse function is valid by plugging in values and making sure the output and input are reversed.
The domain and range of an inverse function are essentially switched from the original function. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function. This is because the input and output are reversed.
To graph an inverse function, you can use a technique called reflection. This involves reflecting the original function's graph over the line y=x. The resulting graph will be the inverse function. It is important to note that some functions may not have an inverse that is a function, in which case the graph will not exist.
Inverse functions are commonly used in real-life applications, such as in finance and economics. They can be used to solve problems involving compound interest, supply and demand, and optimization. Inverse functions can also be used in physics to model motion and in computer science for encryption and decryption algorithms.