Question Number 148452 by mathdanisur last updated on 28/Jul/21

∫_( 1) ^( 4) 2sin^2 x dx + ∫_( 1) ^( 4) (1+cos2x)dx = ?

Answered by puissant last updated on 28/Jul/21

=∫_1 ^4 2(((1−cos2x)/2))+(1+cos2x)dx =∫_1 ^4 (1−cos2x+1+cos2x)dx =∫_1 ^4 2dx = 2[x]_1 ^4 =2(4−1) I = 6...

Commented bymathdanisur last updated on 28/Jul/21

Thank you Ser

Answered by Ar Brandon last updated on 28/Jul/21

1+cos2x=(cos^2 x+sin^2 x)+(cos^2 x−sin^2 x)=2cos^2 x I=∫_1 ^4 2sin^2 xdx+∫_1 ^4 2cos^2 xdx =2∫_1 ^4 (sin^2 x+cos^2 x)dx=2∫_1 ^4 dx=2(4−1)=6

Commented bymathdanisur last updated on 28/Jul/21

Thank you Ser