Integral help

[lovetolearn]

The numbers connected by the ____ lines are either above or below the integral. This question is different from the ones that I have worked simply because of the d/dx and I have not worked much with cos. Thank you for helping!


___________2x
Find (d/dx) ∫ cos^2(t^2)dt
___________0

[HallsofIvy]

The numbers connected by the ____ lines are either above or below the integral. This question is different from the ones that I have worked simply because of the d/dx and I have not worked much with cos. Thank you for helping!


___________2x
Find (d/dx) ∫ cos^2(t^2)dt
___________0

Many people, even going back to Archimedes, worked with forms of the integral and derivatives. What made Newton and Leibniz the "creators" of Calculus was their recognition that these were inverse operations: [tex]\frac{d}{dy}\int_a^y f(t)dt= f(y)[/tex]. Let y= 2x and use the chain rule.

[lovetolearn]

Thank you!!! I solved it and got 2cos^2(4x^2)

[HallsofIvy]

Good!