Answer the following True or False. int(1)/(sec x)dx=ln(sec x)+C True False

Simplify Integral: Let's first simplify the integral. The secant function is the reciprocal of the cosine function, so 1/sec(x) is equivalent to cos(x). Therefore, the integral becomes: ∫cos(x)dxIntegrate Cos(x): Now we integrate cos(x) with respect to x. The antiderivative of cos(x) is sin(x), so: ∫cos(x)dx = sin(x) + CCompare Results: We compare our result with the given statement ln(sec x) + C. Since sin(x) is not equivalent to ln(sec x), the given statement is false.

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Answer the following True or False. $\newline$ $\int \frac{1}{\sec x}\,dx = \ln(\sec x) + C$ $\newline$ True $\newline$ False

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Q. Answer the following True or False.

\newline

\int \frac{1}{\sec x}\,dx = \ln(\sec x) + C

\newline

True

\newline

False

Simplify Integral: Let's first simplify the integral. The secant function is the reciprocal of the cosine function, so $1/\sec(x)$ is equivalent to $\cos(x)$ . Therefore, the integral becomes: $\newline$ $\int \cos(x)\,dx$
Integrate $\cos(x)$ : Now we integrate $\cos(x)$ with respect to $x$ . The antiderivative of $\cos(x)$ is $\sin(x)$ , so: $\newline$ $\int \cos(x)\,dx = \sin(x) + C$
Compare Results: We compare our result with the given statement $\ln(\sec x) + C$ . Since $\sin(x)$ is not equivalent to $\ln(\sec x)$ , the given statement is false.