FAD1014: MATHEMATICS II — Tutorial 5

Centre for Foundation Studies in Science, University of Malaya
Session 2025/2026

Question 1: Area Between Lines

Find area of the regions enclosed by the following curves.

$$x = 3y, \quad x + y = 0, \quad 7x + 3y = 24$$

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

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

(b) $y = x$, $y = 4x$, $y = -x + 2$

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

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

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

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

The area A is the region bounded by the curves [content missing]. Calculate the area A.

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, $x = 0$, $x = 2\pi$

The region R is bounded by the curves [content incomplete] and the line [content incomplete]

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