Area Between Curves

Area Between Curves

Tutorial Questions

1. Find the area of the regions enclosed by the following curves. $$x = 3y, \quad x + y = 0, \quad 7x + 3y = 24$$

2. Sketch the region enclosed by the curves and find its area.

  • (a) $y = 2 + |x - 1|$, $y = -\frac{1}{5}x + 7$
  • (b) $y = x$, $y = 4x$, $y = -x + 2$

3. Find the area of the regions enclosed by the following curves.

  • (a) $y^2 = x$, $x - 2y = 3$
  • (b) $x = 1 - y^2$, $x = y^2 - 1$

4. Calculate the area of the region between the curves $y = 9 - x^2$ and $y = x^2 + 1$ from $x = 0$ to $x = 3$.

5. The area A is the region bounded by the curves $y = \sin x$, $y = \cos x$, $x = 0$, and $x = \frac{\pi}{2}$. Calculate the area A.

6. Sketch and find the area of the region bounded by the following curves and lines.

  • (a) $y = 2x^2$, $x$-axis, $x = 0$, $x = 3$
  • (b) $y = 3x^2$, $y$-axis, $y = 1$, $y = 4$
  • (c) $y = x^3$, $y = -1$, $y = 1$
  • (d) $y = x^3$, $x$-axis, $x = -1$, $x = 1$
  • (e) $y = \sin x$, $x$-axis, $x = 0$, $x = 2\pi$

7. The region R is bounded by the curves $y = x^2$ and $y = 4x - x^2$ and the line $x = 0$.

Source: Soalan Tut 5 FAD1014(25.26)..pdf