This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skippe the skipped part. Tutorial Exercise Evaluate the integral. Step 1 To evaluate the integral, we will first attempt to rewrite the integrand so that involves powers of sine and cosine in a form where we have only c do so, we recall the following double angle formula. cos(2x) = 2 cos²(x) - 1 Applying this gives the following result. -π/6 Step 3 1 0. rπ/6 Step 2 We can now simplify the result as follows. π/6 √ ² / 0 √₁+( F1 √1 + cos(2x) dx √ 1 + cos(2x) dx = Q A √ 1 + (2 cos² (x) - 1) dx 2 π/6 [²²6 √ 1 + ( 2 cos² (x) − 1 - F2 W S = # 3 π/6 *°v@2 2 20 F3 E D $ 4 J Q F4 R FL TC 2 cos² (x) - 1 rπ/6 2√ √ cos²³(x) dx % 5 2 cos² (x) dx ů F5 T MacBook Air < C 6 G F6 Y & f 7 H F7 U * 00 8 DII F8 J 9 F9 K C Applying this gives the following result. π/6 rπ/6 = √²²0 √ ₁ + ( Step 3 Step 2 We can now simplify the result as follows. π/6 1 √1 + cos(2x) dx = :0 F1 √1+ (2 cos²(x) - 1) dx = Q A π/6 √² √2/6 √ cos²(x) dx = √² 1/2 √₂ fő™ π Simplifying the integrand and noting that cos(x) > 0 for 0 ≤ x ≤ 6 2 cos(x) dx = √2 F2 W S 1 +(2 cos² (x) - 1 = = || π/6 2 6₁² °√(² 3 2 π/6 π/6 -√₂/²0 (1 cos(x) Step 4 We have successfully rewritten the integrand in a format that we can easily evaluate. Doing so gives the following result. π/6 1π/6 √₂ √2²². 80 F3 cos(x) E D 10 $ 4 F4 J R 2 F LL 2 cos² (x) - 1 с оро 2 rπ/6 cos(x) % 5 cos(x) allows us to continue as follows. ✓ cos² (x) dx cos² (x) dx O F5 T dx dx G MacBook Air ^ 6 F6 Y & 7 H F7 U * 0 8 J DII F8 ( | 9 T F9 K 0 0