Let a1 and a2 be the two values of a for which the area between these curves and ordinates is S: y = 1 + cos x , y = 1 − cos x , x = π /2 , x = a , 0

Question

Let a1 and a2 be the two values of a for which the area between these curves and ordinates is S: y = 1 + cos x ​ , y = 1 − cos x ​ , x = π /2 , x = a , 0 < a < π , S = 8 sin 2 ( π /16 ) . Find a 1 ​ 3 π ​ + a 2 ​ 3 π ​ . ​

TestHub · Accepted Answer

Use lower evaluation bound a, not 0. For either side of pi/2: $S = 4 [1 - cos (π /4 - a /2)] = 8 sin^{2} (π /8 - a /4) . 0 < a < π : a = π /4, 3 π /4. 3 π / a_{1} + 3 π / a_{2} = 12 + 4 = 16.$

Mathematics - Area Under Curves Question with Solution | TestHub

Doubts & Discussion