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cse63146
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Homework Statement
[tex]\int \sqrt{t^8 + t^6 } dt[/tex]
Homework Equations
The Attempt at a Solution
I'm not sure what to do next, can someone point me in the right direction? Thank you.
cse63146 said:[tex]\int \sqrt{t^8 + t^6 } dt[/tex]
…
I'm not sure what to do next, can someone point me in the right direction? Thank you.
cse63146 said:stuck again (that was fast)
so I got it to this: [tex]\int tan^6 \vartheta (sec^2 \vartheta )[/tex]
do I use integration by parts here?
or would I use a second substitution with u = tan and du = sec^2 ?
cse63146 said:so integration by parts is the following:
[tex]\int f(x)'g(x) \ dx = f(x)g(x) - \int f(x)g'(x) \ dx[/tex]
I chose f'(x) to be [tex]\sqrt{1 + t^2}[/tex] so I could eventually get rid of t^3, but I have no idea how to find f(x)
… so I need to do a trig sub …
tiny-tim said:Either do integration by parts, staying with t, or (possibly slightly easier) just substitute v = 1 + t2, dv = … ?
cse63146 said:dv = 2t
so would it look like this:
[tex]2\int t^2 \sqrt{v} dv[/tex]
would I write dv or dt in this case since I have both t and v.
P.S sorry it took so long to respond, I got sick shortly after this and my fever was gone this morning.
Integration involving square root is a technique used in calculus to find the antiderivative of a function that involves a square root. It is a type of indefinite integral and is used to find the area under a curve.
The main difference between integration involving square root and regular integration is that the former involves functions with a square root, while the latter can involve any type of function. Integration involving square root requires a different set of rules and techniques to solve compared to regular integration.
The steps to solve an integration involving square root problem are as follows:
Integration involving square root is used in various real-life applications, such as calculating the work done by a variable force, finding the center of mass of an object with varying density, and determining the velocity of an object under the influence of gravity. It is also used in engineering, physics, and economics.
One common mistake to avoid when solving integration involving square root problems is forgetting to use substitution and trying to apply regular integration rules. Another mistake is not simplifying the function before attempting to integrate it. It is also important to be careful with signs and constants when using the power rule. It is always recommended to double-check the final solution by differentiating it to ensure it is the correct antiderivative of the original function.