abigaeldalpaca
abigaeldalpaca abigaeldalpaca
  • 31-03-2020
  • Mathematics
contestada

Find F ′(x) for F(x)= ∫ from a= x^2 b=3 for the equation sin(t^2)dx

A. –2xsin(x^4)

B. sin(x^4)

C. –sin(x^4)

D. sin(3^2) – sin(x4)

Respuesta :

LammettHash
LammettHash LammettHash
  • 01-04-2020

[tex]F(x)=\displaystyle\int_{x^2}^3\sin(t^2)\,\mathrm dt=-\int_3^{x^2}\sin(t^2)\,\mathrm dt[/tex]

By the fundamental theorem of calculus, differentiating gives

[tex]F'(x)=-\sin((x^2)^2)(2x)=-2x\sin(x^4)[/tex]

so the answer is A.

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