Quadratic denominators and inverse tangents · Short practice

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Recall

Inverse-tangent integrals — objective 1

Maths4U Original · Short practice

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

Find K in the primitive \(\displaystyle K\arctan (\frac{x}{2})+ C\).

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

Inverse-tangent integrals — objective 1

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{2}{x^{2} + 1}\), on real x.

Find K in the primitive \(\displaystyle K\arctan (\frac{x}{1})+ C\).

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

Inverse-tangent integrals — objective 2

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{3}{x^{2} + 9}\), on real x.

Find f(0).

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

Inverse-tangent integrals — objective 2

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{4}{x^{2} + 16}\), on real x.

Find f(0).

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

Inverse-tangent integrals — objective 3

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{4}{x^{2} + 16}\), on real x.

Find the integral from 0 to 4, divided by π.

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

Inverse-tangent integrals — objective 3

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{2}{x^{2} + 1}\), on real x.

Find the integral from 0 to 1, divided by π.

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

Inverse-tangent integrals — objective 4

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{5}{x^{2} + 25}\), on real x.

Find the integral from 0 to 10.

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

Inverse-tangent integrals — objective 4

Maths4U Original · Short practice

The integrand is \(\displaystyle f(x)=\frac{2}{x^{2} + 1}\), on real x.

Find the integral from 0 to 2.

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.

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