Question

Use part I of the Fundamental Theorem of Calculus to find the derivative of
integral from x to 5 of sin(t^2)dt
I will also show the equation written out below

Answer 1

Use part I of the Fundamental Theorem of Calculus to find the derivative of the integral
\[F(x)=\int\limits\limits_{x}^{5}\sin(t^2)dt\]

Answer 2

\[\int\limits_{x}^{5}\sin(t^2)dt=-\int\limits_{5}^{x}\sin(t^2)dt\]

Answer 3

so F'(x)=-sin(t^2)

Answer 4

so in terms of x would you just write -sin(x^2)?

Answer 5

so F'(x)=-sin(x^2)

Answer 6

yes, my mistake

Answer 7

Thank you so much! I appreciate the help

Answer 8

yw