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Magazine Problem 101
Use the double-angle formulas to evaluate the following integrals. $$ \int \sin ^{2} x d x+\int \cos ^{2} x d x $$
Problem 102
Use the double-angle formulas to evaluate the following integrals. $$ \int \sin ^{2} x \cos ^{2}(2 x) d x $$
Problem 103
Evaluate the definite integrals. Express answers in exact form whenever possible. $$ \int_{0}^{2 \pi} \cos x \sin 2 x d x $$
Problem 104
Evaluate the definite integrals. Express answers in exact form whenever possible. $$ \int_{0}^{\pi} \sin 3 x \sin 5 x d x $$
Problem 105
Evaluate the definite integrals. Express answers in exact form whenever possible. $$ \int_{0}^{\pi} \cos (99 x) \sin (101 x) d x $$
Problem 106
Evaluate the definite integrals. Express answers in exact form whenever possible. $$ \int_{-\pi}^{\pi} \cos ^{2}(3 x) d x $$
Problem 107
Evaluate the definite integrals. Express answers in exact form whenever possible. $$ \int_{0}^{2 \pi} \sin x \sin (2 x) \sin (3 x) d x $$
Problem 108
Evaluate the definite integrals. Express answers in exact form whenever possible. $$ \int_{0}^{4 \pi} \cos (x / 2) \sin (x / 2) d x $$
Problem 109
Evaluate the definite integrals. Express answers in exact form whenever possible. $$ \begin{aligned} &\text { 109. } \int_{\pi / 6}^{\pi / 3} \frac{\cos ^{3} x}{\sqrt{\sin x}} d x \text { (Round this answer to three decimal }\\\ &\text { places.) } \end{aligned} $$
Problem 110
Evaluate the definite integrals. Express answers in exact form whenever possible. $$ \int_{-\pi / 3}^{\pi / 3} \sqrt{\sec ^{2} x-1} d x $$
