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Integrate $-\frac{\pi}{4}$ to $+\frac{\pi}{4}$ $\log(\cos x + \sin x)$

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Add and subtract three or more integers

Full solution

Q. Integrate

-\frac{\pi}{4}

to

+\frac{\pi}{4}

\log(\cos x + \sin x)

Identify Function: Step $1$ : Identify the function to integrate. $\newline$ We need to integrate $\log(\cos(x) + \sin(x))$ from $-\frac{\pi}{4}$ to $\frac{\pi}{4}$ .
Check Symmetry: Step $2$ : Check for symmetry. $\newline$ The function $\log(\cos(x) + \sin(x))$ is not obviously symmetric or antisymmetric, so we proceed with direct integration.
Apply Techniques: Step $3$ : Apply integration techniques. $\newline$ We start integrating $\log(\cos(x) + \sin(x))$ from $-\frac{\pi}{4}$ to $\frac{\pi}{4}$ . This requires substitution or numerical methods since the integral of $\log$ functions combined with trigonometric functions isn't straightforward.
Realize Mistake: Step $4$ : Realize a mistake in the function. $\newline$ The correct function should be $\log(\cos(x) + \sin(x))$ , but it's written as $\log(\cos x + \sin ce)$ , which doesn't make sense mathematically. This is a typo and affects the calculation.

More problems from Add and subtract three or more integers

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\newline

What is the equation for

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\newline

1

\newline

g(x)=-\frac{4}{3}|x|

\newline

g(x)=\frac{4}{3}|x|

\newline

g(x)=-\frac{3}{4}|x|

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g(x)=\frac{3}{4}|x|

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y=-\frac{5}{3}|x|

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y=\frac{3}{5}|x|

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y=-|x-5|+3

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