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Magazine Problem 71
Use an identity to reduce the power of the trigonometric function to a trigonometric function raised to the first power. sin2x = _______
Problem 72
Use an identity to reduce the power of the trigonometric function to a trigonometric function raised to the first power. cos2x = _______
Problem 73
Use an identity to reduce the power of the trigonometric function to a trigonometric function raised to the first power. $$ \int \sin ^{3} x \cos x d x $$
Problem 74
Use an identity to reduce the power of the trigonometric function to a trigonometric function raised to the first power. $$ \int \sqrt{\cos x} \sin x d x $$
Problem 75
Use an identity to reduce the power of the trigonometric function to a trigonometric function raised to the first power. $$ \int \tan ^{5}(2 x) \sec ^{2}(2 x) d x $$
Problem 76
Use an identity to reduce the power of the trigonometric function to a trigonometric function raised to the first power. $$ \int \sin ^{7}(2 x) \cos (2 x) d x $$
Problem 77
Use an identity to reduce the power of the trigonometric function to a trigonometric function raised to the first power. $$ \int \tan \left(\frac{x}{2}\right) \sec ^{2}\left(\frac{x}{2}\right) d x $$
Problem 78
Use an identity to reduce the power of the trigonometric function to a trigonometric function raised to the first power. $$ \int \tan ^{2} x \sec ^{2} x d x $$
Problem 79
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \sin ^{3} x d x $$
Problem 80
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \cos ^{3} x d x $$
