Take the anti derivative of (X^2)/sqrt(1-x)soln'let u=1-x

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In summary, an anti derivative, also known as an indefinite integral, is the inverse operation of a derivative. To find an anti derivative, we can use the power rule, product rule, quotient rule, or chain rule. The power rule for anti derivatives states that the anti derivative of x^n is (x^(n+1))/(n+1), where n is any real number except for -1. We can also use the substitution method by letting u=1-x to find the anti derivative. The anti derivative of (X^2)/sqrt(1-x)soln'let u=1-x is (1/3)(1-x)^3 + C, where C is the constant of integration.
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johnnyboy2005
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take the anti derivative of (X^2)/sqrt(1-x)

soln'... let u=1-x... then -du=dx and x^2 = (1-u)^2 (sub back in)...

this gives me -2*u^(1/2)*(15-10*u+3*u^2) /15... (sorry for lack of proper terms)


anyway, this turns out to be wrong...where did i go wrong here?
 
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  • #2
Try this:

[tex]\int \frac{x^2}{\sqrt{1-x}}dx = -\int \frac{(1-u)^2}{\sqrt{u}}du = -\int u^{-\frac{1}{2}}(1-2u+u^2) du[/tex]

then distribute the [itex]u^{-\frac{1}{2}}[/itex] term over the quadratic and integrate
 
  • #3
yeah...that's what i was getting but it was in a different form. Thanks a lot !1
 

FAQ: Take the anti derivative of (X^2)/sqrt(1-x)soln'let u=1-x

What is an anti derivative?

An anti derivative, also known as an indefinite integral, is the inverse operation of a derivative. It is a mathematical function that, when differentiated, gives the original function.

How do you take an anti derivative?

To take an anti derivative, you need to identify the original function and use the power rule, product rule, quotient rule, or chain rule to find the anti derivative. In this case, we can use the substitution method by letting u=1-x.

What is the power rule for anti derivatives?

The power rule for anti derivatives states that the anti derivative of x^n is (x^(n+1))/(n+1), where n is any real number except for -1. In this case, we have x^2, so the anti derivative is (x^3)/3.

How do you use substitution to find an anti derivative?

To use substitution, we choose a new variable, u, to replace part of the original function. Then, we find the anti derivative of the new function in terms of u. Finally, we substitute the original variable back into the equation to get the final anti derivative. In this case, we let u=1-x and find the anti derivative of (u^2)/sqrt(u).

What is the anti derivative of (X^2)/sqrt(1-x)soln'let u=1-x?

The anti derivative of (X^2)/sqrt(1-x)soln'let u=1-x is (1/3)(1-x)^3 + C, where C is the constant of integration. We use the substitution method and the power rule for anti derivatives to arrive at this solution.

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