Reciprocal and logarithmic integration · Short practice

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Recall

Reciprocal-linear integrals — objective 1

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{4}{x + 3}\), 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.

Fresh review variant

Reciprocal-linear integrals — objective 1

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{5}{2 x + 4}\), 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.

Method

Reciprocal-linear integrals — objective 2

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{5}{2 x + 4}\), 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.

Fresh review variant

Reciprocal-linear integrals — objective 2

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{2}{3 x + 1}\), on \(\displaystyle x>- \frac{1}{3}\).

Find f(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Reciprocal-linear integrals — objective 3

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{2}{3 x + 1}\), on \(\displaystyle x>- \frac{1}{3}\).

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.

Fresh review variant

Reciprocal-linear integrals — objective 3

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{3}{x + 2}\), 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.

Check understanding

Reciprocal-linear integrals — objective 4

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{3}{x + 2}\), 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.

Fresh review variant

Reciprocal-linear integrals — objective 4

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{4}{2 x + 3}\), on \(\displaystyle x>- \frac{3}{2}\).

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.

Try written exam-style problems →