Valishati
Valishati Valishati
  • 25-05-2020
  • Mathematics
contestada

Suppose f(x)= INT(1,x^2) ((sin(t))/t)dt. What is f'(x)?

Suppose fx INT1x2 sinttdt What is fx class=

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sqdancefan
sqdancefan sqdancefan
  • 31-05-2020

Answer:

  see below

Step-by-step explanation:

The fundamental rule of calculus tells you that for ...

  [tex]\displaystyle f(x)=\int^{a(x)}_b {u(t)} \, dt \\\\f'(x)=u(a(x))a'(x)-u(b(x))b'(x)[/tex]

Then, for the specific case in this problem, we have ...

  a(x) = x^2; a'(x) = 2x

  b(x) = 1; b'(x) = 0

  f'(x) = sin(x^2)/x^2·(2x)

  f'(x) = 2sin(x^2)/x . . . . . matches choice D

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