Gregg O. answered • 06/23/16

For 3 semesters in college, top of my class in Calculus

In using u-subs, we often look for a function and its derivative together inside the integral. What is the derivative of 3 + t

^{2}? Do you see it in the function? What happens if you chooseu = 3 + t

^{2}?Gregg O.

When making a u-sub in a definite integral, it's common to leave things in terms of u after integrating. In order to do this, the upper and lower limits are re-written. For example, say the lower and upper limits of integration are 1 and 3, respectively.

Given our u = 3 + t

^{2}, the new lower limit becomes 3 + (1)^{2}= 4, while the new upper limit becomes 3 + (3)^{2}= 12. What we're really doing is figuring out what u is equal to when t is equal to the upper and lower limits, and substituting these new values in place of the old limits of integration.Use your actual values of a and b when solving the problem, and remember that unlike indefinite integrals with u-subs, you don't return to an expression in x before plugging in the upper and lower limits when changing the limits of integration to u(a) and u(b).

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06/23/16

M K.

Thanks a lot! This was really helpful!

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06/24/16

M K.

06/23/16