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Exercise 13

Avg difficulty 2.5

Let f(t)=te−2tf(t) = te^{-2t} and F(x)=∫0xf(t) dtF(x) = \int_0^x f(t) \, dt.

  1. Determine F′(x)F'(x).

  2. Use the First FTC to find a formula for FF that does not involve an integral.

  3. Is FF an increasing or decreasing function for x>0x \gt 0? Why?

Boelkins, Active Calculus, §5.4 Integration by parts, Exercise 13

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Adapted from Active Calculus © 2012–2025 Matthew Boelkins. Licensed under CC BY-SA 4.0. Source: Active Calculus. Imported at revision dc86ba3.