anonymous
  • anonymous
What does it mean when I'm asked to solve an integral of a function of t between within a section with borders in term of x? See attached question for example.
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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ash2326
  • ash2326
What you have to do is find F(x) first then differentitate it , when you integrate the function in t and we are given the limits in x , so it'll become a function in x You can use the method to easily evaluate F'(x) without integrating
ash2326
  • ash2326
\[F(x)=\int\limits_{0}^{x^2+2x} (6+ \cos^2 t) dt\] let's differentitate with respect to x \[F'(x)= [6+\cos^2 (x^2+2x)](d/dx (x^2+2x))-[6+\cos^2 (0)](d/dx (0))\] substitute upper limit in t and product of this with the derivative of upper limit - the lower limit in function and product of it with the lower limit's derivative . you'll get \[F'(x)= (2x+2)( 6+ \cos^2 (x^2+2x))-0\]

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ash2326
  • ash2326
sorry it was cos t^2, then you'll get \[F'(x)= (2x+2)(6+ \cos (x^2+2x)^2)\]
anonymous
  • anonymous
Ok I think I understand. Thanks a lot. I've been trying to do this all day.
ash2326
  • ash2326
no problem, just remember the method, you'd be able to solve any proble like this
ash2326
  • ash2326
*problem

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