Use the Fundamental Theorem of Calculus to evaluate the following definite integral.
\[
\int_{1}^{4} \frac{3}{t} d t
\]
\[
\int_{1}^{4} \frac{3}{t} d t=\square
\]
(Type an exact answer.)

Answer

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Answer

The value of the definite integral is \(\boxed{3 \ln(4)}\)

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Step 1 ：The Fundamental Theorem of Calculus states that if a function f is continuous over the interval [a, b] and F is an antiderivative of f on [a, b], then the definite integral of f from a to b is equal to F(b) - F(a).

Step 2 ：In this case, the function \(f(t) = \frac{3}{t}\) is continuous over the interval [1, 4] and its antiderivative \(F(t) = 3\ln|t|\).

Step 3 ：So, we need to evaluate \(F(4) - F(1)\).

Step 4 ：The value of the definite integral is \(\boxed{3 \ln(4)}\)

Use the Fundamental Theorem of Calculus to evaluate the following definite integral.\[\int_{1}^{4} \frac{3}{t} d t\]\[\int_{1}^{4} \frac{3}{t} d t=\square\](Type an exact answer.)

Answer

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Use the Fundamental Theorem of Calculus to evaluate the following definite integral.
\[
\int_{1}^{4} \frac{3}{t} d t
\]
\[
\int_{1}^{4} \frac{3}{t} d t=\square
\]
(Type an exact answer.)