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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

Question

g

can be thought of as a scaled version of

f(x)=|x|

\newline

What is the equation for

g(x)

\newline

1

\newline

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

\newline

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

\newline

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

\newline

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

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Question

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What is the equation of the new graph?

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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

\newline

y=|x-3|+5

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Question

\$ 200

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40 h+80 t=400

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80 h+40 t=200

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5 h+2.5 t=200

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What will Ari think about the amount of caramel in Freeze Zone's milkshakes?

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(A) Freeze Zone's milkshakes have too much caramel.

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(B) Freeze Zone's milkshakes have too little caramel.

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(C) Freeze Zone's milkshakes are just right.

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Whose scrambled eggs have a stronger salsa taste?

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(A) Lashawn's eggs

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(B) Gilberta's eggs

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(C) The dishes of scrambled eggs have equal salsa tastes.

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