- #1
Stochastic13
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Homework Statement
How do you integrate: 1/3(x^2(50 - x^2)^(3/2))
Homework Equations
The Attempt at a Solution
I tried by parts with no luck :(
Do you mean: [itex]\displaystyle \int{\frac{1}{3x^2(50-x^{2})^{3/2}}}\,dx\ ?[/itex]Stochastic13 said:Homework Statement
How do you integrate: 1/3(x^2(50 - x^2)^(3/2))
Homework Equations
The Attempt at a Solution
I tried by parts with no luck :(
The formula for integrating 1/3(x^2(50 - x^2)^(3/2)) is ∫1/3(x^2(50 - x^2)^(3/2))dx = 1/10(50-x^2)^(5/2) + C.
To solve this integral, you can use the substitution method or integration by parts. Both methods require some algebraic manipulation and may involve using trigonometric identities.
Yes, this integral can be simplified by using trigonometric identities such as sin^2(x) + cos^2(x) = 1 to combine terms and make the integration process easier.
The domain of this integral is all real numbers, as there are no restrictions on the values of x in the given function.
Yes, this integral can be solved using a calculator with an integral function. However, it is always important to double-check the result and make sure it is correct.