Integral for Area Between Two Curves

Question

Which of the following integrals represents the area of the region enclosed by the graphs of $$f(x)=\cos(x)$$ and $$g(x)=\sin(x)$$ on the interval $$\left[0,\frac{\pi}{4}\right]$$?

Accepted Answer

$$\int_{0}^{\frac{\pi}{4}} \Bigl(\cos(x)-\sin(x)\Bigr)\,dx$$

Answer

$$\frac{1}{\frac{\pi}{4}}\int_{0}^{\frac{\pi}{4}} \Bigl(\cos(x)-\sin(x)\Bigr)\,dx$$

Answer

$$\int_{0}^{\frac{\pi}{4}} \Bigl(\cos(x)+\sin(x)\Bigr)\,dx$$

Answer

$$\int_{0}^{\frac{\pi}{4}} \Bigl(\sin(x)-\cos(x)\Bigr)\,dx$$

Integral for Area Between Two Curves

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