Q1
Answer
Evaluate $$\displaystyle\int_1^3 -3x^2 + 17x - 10\ \mathrm{d}x$$
$22$
Q2
Answer
Evaluate $$\displaystyle\int_{-3}^{-1} 2x^3 + 7x^2 - 4x\ \mathrm{d}x$$
$\dfrac{110}{3}$
Q3
Answer
Evaluate $$\displaystyle\int_0^4 -x^4 + 7x^3 - 11x^2 + 5x\ \mathrm{d}x$$
$\dfrac{728}{15}$
Q4
Answer
Evaluate $$\displaystyle\int_{-4}^{-1} \dfrac{8}{x^2}\ \mathrm{d}x$$
$6$
Q5
Answer
Given $$\displaystyle\int_2^k 2x^2 - 5\ \mathrm{d}x = 63$$ find $k$.
$5$
Q6
Answer
Given $$\displaystyle\int_k^3 \dfrac{4x^2 + 3}{x^2}\ \mathrm{d}x = \dfrac{9}{2}$$ find $k$.
$2$
Q7
Answer
Find the exact area bound by the curve $y = x^3 - 2x - 7$, the lines $x = 1$ and $x = 2$ and the $x$ axis.
$6.25$
Q8
Answer
Find the exact area bound by the curve $y = 3x + \dfrac{6}{x^2} - 5$, the lines $x = 1$ and $x = 3$ and the $x$ axis.
$6$
Q9
Answer
Find the exact area bound by the curve $y = 2x^3 - 3x^2 - 1$, the lines $x = 0$ and $x = 1$ and the $x$ axis.
$1.5$
Q10
Answer
Find the exact area bound by the curve $y = 4x\sqrt{x} - 6$, the lines $x = 0$ and $x = 1$ and the $x$ axis.
$4.4$
Q11
Answer
Shown below is the curve with equation $$y = x^2 - 5x + 4$$ Find the area of the shaded region.
$3$
Q12
Answer
Shown below is the curve with equation $$y = 2 - 3x^2 + 5x$$ Find the area of the shaded region.
$10.5$
Q13
Answer
Find the area of the finite region bound by the curve $y = (3-x)(1+x)$ and the $x$ axis.
$\dfrac{32}{3}$
Q14
Answer
Find the area of the finite region bound by the curve $y = x(x-4)^2$ and the $x$ axis.
$\dfrac{64}{3}$
Q15
Answer
Shown below is the curve with equation $$y = x^3 - x$$ Find the area of the shaded region.
$0.5$
Q16
Answer
Shown below is the curve with equation $$y = x^3 - 6x^2 + 5x$$ Find the coordinates of the points of intersection with the axes and hence find the area of the shaded region.
$32.75$
Q17
Answer
Find the area of the finite region bound by the curve $y = 2x^2 - 3x^3$ and the $x$ axis.
$\dfrac{4}{81}$
Q18
Answer
The area under the curve with equation $y = 3x^2 - 2x + 2$ between $x = 0$ and $x = k$ is $8$. Given that the curve never crosses the $x$ axis, find $k$.
$2$
Q19
Answer
Shown below is the curve $y = 9 - x^2 + 4x$. Find the area of the shaded region.
$\dfrac{32}{3}$
Q20
Answer
Shown below is the curve $y = x^3 - 3x^2 + 2x + 2$ and the line $y = 2x$. They intersect at $(1, 2)$. Find the area of the shaded region.
$1.25$
Q21
Answer
Shown below is the curve $y = 2x^3 - 3x^2 + 5$ and the line $y = 4x$. They intersect at $(1, 4)$. Find the area of the shaded region.
$2.5$
Q22
Answer
Shown below is the curve $y = x^3 + 1$ and the line $y = 6 - 4x$. They intersect at $(1, 2)$. Find the area of the shaded region.
$1.75$
Q23
Answer
Shown below is the curve $y = (x-2)(x+3)$ and the line $y = 6 - 3x$. Find the area of the shaded region.
$\dfrac{40}{3}$
Q24
Answer
Shown below is the curve $y = x^3 + 3x^2 - 5x + 4$ and the line $y = 26 - 6x$. They intersect at $(2, 14)$. Find the area of the shaded region.
$\dfrac{79}{3}$