The curves $f(x)=\sin x$ and $g(x)=\cos x$ intersect periodically.
Determine the area of the region bounded by these curves between $x=\frac{\pi}{4}$ and $x=\frac{5 \pi}{4}$.

Question

The curves $f(x)=\sin x$ and $g(x)=\cos x$ intersect periodically.
Determine the area of the region bounded by these curves between $x=\frac{\pi}{4}$ and $x=\frac{5 \pi}{4}$.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the area between the curves $f(x)=\sin x$ and $g(x)=\cos x$ from $x=\frac{\pi}{4}$ to $x=\frac{5\pi}{4}$, we need to integrate the difference of the functions over this interval. ‖ ‖ step 2 ⋮ The integral of the difference $f(x) - g(x)$ from $x=\frac{\pi}{4}$ to $x=\frac{5\pi}{4}$ is given by $\int_{\pi/4}^{5\pi/4} (\sin x - \cos x) \, dx$. ‖ ‖ step 3 ⋮ Using the asksia-ll calculator, the result of the integral is $2\sqrt{2}$. ‖ ∻Answer∻ ⚹ $2\sqrt{2}$ ⚹ ∻Key Concept∻ ⚹Area between curves⚹ ∻Explanation∻ ⚹The area between two curves from $a$ to $b$ is found by integrating the difference of the functions, $f(x) - g(x)$, from $a$ to $b$.⚹◊What is the equation for finding the area between two intersecting periodic curves in the given interval?⍭ Generate me a similar question◊

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