Question Type 5: Area between two curves with changing dominance Exercises

Compute the area between the curves $y=\sin x$ and $y=\cos x$ for $0 \le x \le \pi$.

Determine the area enclosed between $y = x^3$ and $y = 2x$ on $-2 \le x \le 2$.

Determine the area between $y = 4x - x^2$ and $y = x$ for $0 \le x \le 4$.

Determine the area between $y = x^2 - 4$ and $y = 2x - 4$ for $0 ≤ x ≤ 4$.

Compute the area enclosed between $y = \cos x$ and $y = \sin x$ for $0 \le x \le \tfrac{\pi}{2}$.

Find the area enclosed between the curve $y = x^3 - x$ and the $x$-axis for $-1 \le x \le 1$.

Find the area between the curves $y = x^2$ and $y = 4 - x$ for $0 \le x \le 4$.

Calculate the area between the curves $y = x^3 - x^2 - x$ and $y = x$ over $-1 \le x \le 2$.

Calculate the area between the curves $y = x^2$ and $y = x$ for $0 \le x \le 2$.

Find the area between the curves $y = x^2 - 2x$ and $y = 2 - x^2$ for $0 \le x \le 3$.

Compute the area between $y = x^2$ and $y = 4 - x^2$ for $-3 \le x \le 3$.

Find the area between the curves $y = 3x - x^2$ and $y = x^2 - x$ over $0 \le x \le 3$.