- #1

Echo 6 Sierra

- 25

- 1

If you could, please guide me and don't spell out the answer.

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- Thread starter Echo 6 Sierra
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- #1

Echo 6 Sierra

- 25

- 1

If you could, please guide me and don't spell out the answer.

- #2

LeonhardEuler

Gold Member

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[tex]\int_{a}^{b}f(x)dx=F(b)-F(a)[/tex]

where F(x) is an antiderivative of f(x). The other is that

[tex]\frac{d}{dx}\int_{0}^{x} f(t)dt=f(x)[/tex]

I think they mean for you to use the latter along with the product rule for differentiation.

- #3

HallsofIvy

Science Advisor

Homework Helper

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but the derivative of [tex]\int_0^x f(t)dt[/tex] is just f(x).

- #4

Echo 6 Sierra

- 25

- 1

Sorry, got lazy with the la tex.

- #5

HallsofIvy

Science Advisor

Homework Helper

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Representing, for the moment, [itex] \int^x_0 tan^2 2tdt[/itex] as "f(x)", the problem is to differentiate g(x)f(x) and its derivative is, of course, g'(x)f(x)+ g(x)f'(x) (the product rule).

By the Fundamental Theorem of Calculus (one of them, anyway),

f'(x)= tan

So your derivative is

[tex]g'(x)\int^x_0 tan^2 2tdt+ g(x)tan^2(2x)[/tex]

- #6

Echo 6 Sierra

- 25

- 1

...good grief...I have a long way to go. Thank you.

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