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Recall
Integration using partial fractions — objective 1
Maths4U Original · Short practice
For \(\displaystyle x\ge 0\), consider \(\displaystyle f(x)=\frac{\left(2 x + 11\right) \left(3 x + 8\right)}{\left(x + 1\right) \left(x + 4\right) \left(x + 6\right)}\). Use the decomposition \(\displaystyle \frac{A}{x+ 1}+ \frac{B}{x+ 4}+ \frac{C}{x+ 6}\).
Find A in the stated decomposition.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Integration using partial fractions — objective 1
Maths4U Original · Short practice
For \(\displaystyle x\ge 0\), consider \(\displaystyle f(x)=\frac{7 x^{2} + 63 x + 134}{\left(x + 2\right) \left(x + 5\right)^{2}}\). Use the decomposition \(\displaystyle \frac{A}{x+ 2}+ \frac{B}{x+ 5}+ \frac{C}{(x+ 5)^{2}}\).
Find A in the stated decomposition.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Method
Integration using partial fractions — objective 2
Maths4U Original · Short practice
For \(\displaystyle x\ge 0\), consider \(\displaystyle f(x)=\frac{7 x^{2} + 63 x + 134}{\left(x + 2\right) \left(x + 5\right)^{2}}\). Use the decomposition \(\displaystyle \frac{A}{x+ 2}+ \frac{B}{x+ 5}+ \frac{C}{(x+ 5)^{2}}\).
Find B in that decomposition.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Integration using partial fractions — objective 2
Maths4U Original · Short practice
For \(\displaystyle x\ge 0\), consider \(\displaystyle f(x)=\frac{3 \left(3 x^{2} + 5 x + 63\right)}{\left(x + 3\right) \left(x^{2} + 36\right)}\). Use the decomposition \(\displaystyle \frac{A}{x+ 3}+ \frac{Bx+ C}{x^{2}+ 36}\).
Find B in that decomposition.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Apply
Integration using partial fractions — objective 3
Maths4U Original · Short practice
For \(\displaystyle x\ge 0\), consider \(\displaystyle f(x)=\frac{3 \left(3 x^{2} + 5 x + 63\right)}{\left(x + 3\right) \left(x^{2} + 36\right)}\). Use the decomposition \(\displaystyle \frac{A}{x+ 3}+ \frac{Bx+ C}{x^{2}+ 36}\).
Find C in that decomposition.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Integration using partial fractions — objective 3
Maths4U Original · Short practice
For \(\displaystyle x\ge 0\), consider \(\displaystyle f(x)=\frac{2 \left(4 x^{2} + 30 x + 41\right)}{\left(x + 1\right) \left(x + 4\right) \left(x + 6\right)}\). Use the decomposition \(\displaystyle \frac{A}{x+ 1}+ \frac{B}{x+ 4}+ \frac{C}{x+ 6}\).
Find C in that decomposition.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Check understanding
Integration using partial fractions — objective 4
Maths4U Original · Short practice
For \(\displaystyle x\ge 0\), consider \(\displaystyle f(x)=\frac{2 \left(4 x^{2} + 30 x + 41\right)}{\left(x + 1\right) \left(x + 4\right) \left(x + 6\right)}\). Use the decomposition \(\displaystyle \frac{A}{x+ 1}+ \frac{B}{x+ 4}+ \frac{C}{x+ 6}\).
Find the definite integral from 0 to 1.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
Integration using partial fractions — objective 4
Maths4U Original · Short practice
For \(\displaystyle x\ge 0\), consider \(\displaystyle f(x)=\frac{4 x^{2} + 39 x + 89}{\left(x + 2\right) \left(x + 5\right)^{2}}\). Use the decomposition \(\displaystyle \frac{A}{x+ 2}+ \frac{B}{x+ 5}+ \frac{C}{(x+ 5)^{2}}\).
Find the definite integral from 0 to 1.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.