Question Number 102066 by bramlex last updated on 06/Jul/20

(1)∫ ((cos (ax) dx)/(√(sin ax−b)))  (2) (D^3 +2D^2 +D)y = e^(2x) +x^2 −x  (3)the area between the curves  y = (2/x) and y = −x+3

Answered by bemath last updated on 06/Jul/20

(1)∫((cos (ax) dx)/(√(sin ax−b))) =(1/a)∫ ((d(sin ax−b))/(√(sin ax−b)))  = (2/a)(√(sin ax−b)) + C

Answered by PRITHWISH SEN 2 last updated on 06/Jul/20

3)  the intersection point (2,1) and (1,2)  ∴ the area between the curves  ∫_1 ^2 (−x+3)dx−∫_1 ^2 (2/x)dx =(3/2)−ln4   please check

Answered by Dwaipayan Shikari last updated on 06/Jul/20

(2/x)=−x+3  x^2 −3x+2=0  x=1or2  point of intersecting (1,2) , (2,1)  ∫_1 ^2 (2/x)+x−3  2log2+(3/2)−3=∣2log2−(3/2)∣=(3/2)−2log2