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2021 YIJC P1 Q5 It is given that $O$ is the origin and $A$ is the point on the curve $y=x{{text{e}}^{x}}$ where $x=3$. The region bounded by the curve $y=x{{text{e}}^{x}}$and
2021 NYJC P1 Q2 (i) On the same axes, sketch the curves with equations, $y=left| frac{ax-3a+2}{3-x} right|$ and $y=frac{a}{3}x$, where $a>1$, giving the equations of the asymptotes and the coordinates
2022 EJC P1 Q1 On the same axes, sketch the graphs of $y=left| x-a right|$ and $y=left| x-b right|$, where $a$ and $b$ are constants such that $0<a<b$. You should
2022 ASRJC P1 Q6 (b) (i) Sketch the graphs of $y=left| {{x}^{2}}-7 right|$ and $y=x+5$ on the same diagram. Indicate clearly the $x$-intercepts and the values of $x$ where the
2019 JPJC P1 Q9 Find (a) $int{frac{{{text{e}}^{frac{1}{x}}}}{{{x}^{2}}},text{d}x}$, [2] (b) $int{cos kxcos left( k+2 right)x,text{d}x}$, where $k$ is a positive constant, [2] (c) $int{x{{tan }^{-1}}left( 3x right),,text{d}x}$. [6] Suggested Video Solutions
2022 RI P1 Q8 A curve $C$ is defined by $y=frac{{{left( ln x right)}^{4}}}{sqrt{x}}$ where $0<x<10$. (i) Find the exact volume generated when the area bounded by $C$, the $x$-axis
2022 VJC Promo Q10 [Modified] (a) (i) Show that $9x$ can be expressed as $Aleft( 12-18x right)+B$, where $A$ and $B$ are constants to be determined. [1] (ii) Without the
2023 SAJC BT P2 Q3 (i) Show that $int_{0}^{frac{pi }{2}}{{{e}^{2y}}cos 2y}text{ d}y=aleft( {{e}^{pi }}+1 right)$ , where $a$ is a constant to be determined. [5] (ii) A curved container has
Home Techniques of Integration Practice 4 Q19 By considering $x=4cos theta $ where $0le theta le pi $, find $int{sqrt{16-{{x}^{2}}},text{d}x}$. Suggested Video and handwritten Solutions Written by Did You Enjoy This
NJC Inequalities Tutorial Q4 Solve the following inequalities (a) $left| x-frac{2}{x} right|<2$, where $xin mathbb{R}$ and $xne 0$, without the use of calculator. (b) $frac{1}{{{left( x-1 right)}^{2}}}ge left| 3x-5 right|$,