Steven N.
asked • 08/27/23Calculus II problem with integrals
This is for my daughter. She got all but this one and I am no help.
Find integral of (7sec^2(t)-7t^3)dx
I appreciate the help with this.
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2 Answers By Expert Tutors
Jonathan T. answered • 08/28/23
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Thanks!
Author Jonathan David
Bradford T. answered • 08/27/23
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Retired Engineer / Upper level math instructor
I'm guessing you meant dt instead of dx.
∫7sec2(t)-7t3 dt = 7∫sec2(t)dt - 7∫t3dt = 7tan(t)+7t4/4 + C
Steven N.
I am looking at the problem and it says dx. That is what is stumping her
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08/27/23
Luke J.
Are you sure there isn't a missing piece of information relating x and t? It seems like it may have been the result of some sort of substitution that hasn't been shown.
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08/27/23
Bradford T.
There needs to be a way to find dx/dt since we need integral of y(t)(dx/dt)dt. That requires an x(t).
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08/27/23
Steven N.
both she and I agree with you both. But there is no other information given. The assignment is an online assignment. I have no way of posting a photo of the question/problem. She tried to get another similar problem to work and it gave the same scenario of the 2nd variable to solve for
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08/27/23
Steven N.
I have looked at all 28 questions, this is the only problem with a 2nd variable with no other information to help solve for the 2nd variable.
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08/27/23
Roger R.
tutor
If there's no dependence between t and x, f(t) = 7sec²t−7t³ is constant while x varies. If so, ∫f(t)dx = ∫f(t)⋅1dx = f(t)⋅∫1dx = f(t)⋅(x +C).
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08/28/23
Steven N.
Turns out it was a typo. Worked it as such and answer was correct. Thanks for everyone’s input
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08/28/23
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Bradford T.
Was there a parametric or some other relationship given between x and t?08/27/23