# How do you use the Fundamental Theorem of Calculus to find the derivative of #int 6*(sin(t))^2 dt# from 1 to e^x?

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To find the derivative of ( \int_{1}^{e^x} 6\sin^2(t) , dt ) using the Fundamental Theorem of Calculus, we can first express it as an antiderivative. Then, we differentiate the result with respect to ( x ).

Let ( F(x) = \int_{1}^{e^x} 6\sin^2(t) , dt ).

By the Fundamental Theorem of Calculus, ( F'(x) = 6\sin^2(e^x) \cdot (e^x)' ).

Using the chain rule, ( (e^x)' = e^x ).

Thus, ( F'(x) = 6\sin^2(e^x) \cdot e^x ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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