Question Type 2: Integrals for total area (using absolute value) Exercises

Find the total area between the curve $y = x^3 - x^2 - 32x + 60$ and the $x$-axis on $[-6,5]$.

Find the total area enclosed by the curve $y = x^2 - 4x$ and the x-axis for $0 \le x \le 5$.

Find the total area between the curve $y = x^3 - x$ and the x-axis on $[-2,2]$.

Calculate the total area between the curve $y = x^3$ and the x-axis over $[-2,2]$.

Determine the total area between $y = \cos x$ and the $x$-axis on $[-\tfrac{\pi}{2},\tfrac{3\pi}{2}]$. [5 marks]

Compute the total area between the curve $y = x^2 - x - 6$ and the x-axis on $[-2,4]$.

Find the total area between the curve $y = x^2 - 9$ and the x-axis on the interval $[1, 4]$.

Find the total area between $y = x^3 - 6x$ and the x-axis on $[-3,3]$.

Find the total area between the curve $y = x^2 - 4$ and the x-axis on the interval $[-3,3]$.

Determine the total area enclosed by $y = \sin(2x)$ and the x-axis on $[0,\pi]$.

Compute the total area between $y = x^4-4x^2$ and the $x$-axis on $[-3,3]$.

Calculate the total area enclosed by $y = \sin x$ and the x-axis on $[0,2\pi]$.