Squared trigonometric integrals · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Integrating squared trigonometric functions — objective 1

Maths4U Original · Short practice

The integrand is \(f(x)=5 \sin^{2}{\left(2 x \right)} + 11 \cos^{2}{\left(2 x \right)}\), on real x.

Find the coefficient of x in a primitive.

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

Integrating squared trigonometric functions — objective 1

Maths4U Original · Short practice

The integrand is \(f(x)=2 \sin^{2}{\left(3 x \right)} + 7 \cos^{2}{\left(3 x \right)}\), on real x.

Find the coefficient of x in a primitive.

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

Integrating squared trigonometric functions — objective 2

Maths4U Original · Short practice

The integrand is \(f(x)=2 \sin^{2}{\left(3 x \right)} + 7 \cos^{2}{\left(3 x \right)}\), on real x.

Write a primitive as Kx+L sin(6x)+C. Find L.

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

Integrating squared trigonometric functions — objective 2

Maths4U Original · Short practice

The integrand is \(f(x)=3 \sin^{2}{\left(x \right)} + 8 \cos^{2}{\left(x \right)}\), on real x.

Write a primitive as Kx+L sin(2x)+C. Find L.

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

Integrating squared trigonometric functions — objective 3

Maths4U Original · Short practice

The integrand is \(f(x)=3 \sin^{2}{\left(x \right)} + 8 \cos^{2}{\left(x \right)}\), on real x.

Find the integral from 0 to \(\displaystyle \frac{\pi }{2}\), 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

Integrating squared trigonometric functions — objective 3

Maths4U Original · Short practice

The integrand is \(f(x)=4 \sin^{2}{\left(2 x \right)} + 9 \cos^{2}{\left(2 x \right)}\), on real x.

Find the integral from 0 to \(\displaystyle \frac{\pi }{4}\), 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.

Check understanding

Integrating squared trigonometric functions — objective 4

Maths4U Original · Short practice

The integrand is \(f(x)=4 \sin^{2}{\left(2 x \right)} + 9 \cos^{2}{\left(2 x \right)}\), 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

Integrating squared trigonometric functions — objective 4

Maths4U Original · Short practice

The integrand is \(f(x)=5 \sin^{2}{\left(3 x \right)} + 10 \cos^{2}{\left(3 x \right)}\), 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.

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