Integration Paper 3 .pdf

About this worksheet

This is the Mathematics worksheet. It is a free worksheet for revision.

More Mathematics papers

• Textbook19 MB
• Textbook14 MB
• Textbook18 MB
• Paper 2 Question Paper81 KB
• Textbook13 MB
• Notes111 KB
• Question Paper332 KB
• Revision Pack399 KB

Other years: Mathematics

• 2021 February Worksheet199 KB
• 2021 January Worksheet190 KB
• 2023 2nd Term Worksheet357 KB

Text from the first page

INTEGRATION
1. Carry out the following indefinite integrations, and state the values of x for which your answer is valid.
a). $\quad \frac{1}{2} \mathrm{dx}$
b). $\frac{1}{x-1} d x$
c). $\frac{1}{1-\mathrm{x}} \mathrm{dx}$
d). $\frac{1}{4 x+3} d x$
e). $\frac{4}{1-2 x} d x$
f). $\frac{4}{1+2 \mathrm{x}} \mathrm{dx}$
g). $\frac{4}{-1-2 x} d x$
h). $\frac{4}{2 x-1} d x$
2. Calculate the area under the graph of $y=1 / x$ from
a. $x=3$ to $x=6$
b. $x=4$ to $x=8$
c. $x=1 / 2$ to $x=1$
d. $x=a$ to $x=2 a, \quad a>0$
3. Calculate the areas under the following graphs
a. $\quad y=\frac{1}{x+2} \quad$ from $x=-1$ to $x=0$
b. $\quad y=\frac{1}{2 x-1}$ from $x=2$ to $x=5$
c. $\quad y=\frac{2}{3 x-5}$ from $x=4$ to $x=6$
d. $\quad \mathrm{y}=\frac{\mathrm{e}}{\mathrm{ex}-7}$ from $\mathrm{x}=4$ to $\mathrm{x}=5$
e. $\quad \mathrm{y}=\frac{1}{-\mathrm{x}-1}$ from $\mathrm{x}=-3$ to $\mathrm{x}=-2$