True Or False Again and again and again

Calculus Level 2

F ( x ) = ∫ − 2 3 x sin ⁡ ( t ) d t \large F(x) = \displaystyle \int_{-2}^{3x} \sin(t)\, dt True or false : F ′ ( x ) = sin ⁡ ( 3 x ) F '(x) = \sin (3x) .

False True

Franz Pabilona by Franz Pabilona , 21, Philippines

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1 solution

Franz Pabilona
May 1, 2016

False.

Note that the upper limit in the integral above is 3x and not x, hence the integral above has the form

F(x) = ∫ -2u(x) f(t) dt

Using the chain rule, we can write

F '(x) = dF / du * du / dx = 3 sin (3x)

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