Reciprocal and logarithmic integration: check 1
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{4}{x + 3}\), on \(x>-3\).
Find K in the primitive K ln(1x+3)+C on the stated domain.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Reciprocal and logarithmic integration: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{5}{2 x + 4}\), on \(x>-2\).
Find K in the primitive K ln(2x+4)+C on the stated domain.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Reciprocal and logarithmic integration: check 2
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{5}{2 x + 4}\), on \(x>-2\).
Find f(0).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Reciprocal and logarithmic integration: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{2}{3 x + 1}\), on \(x>- \frac{1}{3}\).
Find f(0).
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Reciprocal and logarithmic integration: check 3
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{2}{3 x + 1}\), on \(x>- \frac{1}{3}\).
The linear expression \(3x+1\) increases from 2 to 8. The corresponding definite integral of f is q ln2. Find q.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Reciprocal and logarithmic integration: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{3}{x + 2}\), on \(x>-2\).
The linear expression \(1x+2\) increases from 2 to 8. The corresponding definite integral of f is q ln2. Find q.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Reciprocal and logarithmic integration: check 4
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{3}{x + 2}\), on \(x>-2\).
Find the x-coordinate of the pole.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Reciprocal and logarithmic integration: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
The integrand is \(f(x)=\frac{4}{2 x + 3}\), on \(x>- \frac{3}{2}\).
Find the x-coordinate of the pole.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.