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-

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

(1) \int \frac{\cos (ax) dx}{\sqrt{\sin ax - b}}

(2) (D^{3} + {2 D}^{2} + D) y = e^{2 x} + x^{2} - x

(3) the area between the curves

y = \frac{2}{x} and y = - x + 3

Answered by bemath last updated on 06/Jul/20

(1) \int \frac{\cos (a x) d x}{\sqrt{\sin a x - b}} = \frac{1}{a} \int \frac{d (\sin a x - b)}{\sqrt{\sin a x - b}}

= \frac{2}{a} \sqrt{\sin a x - 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

\int_{1}^{2} (- x + 3) dx - \int_{1}^{2} \frac{2}{x} dx = \frac{3}{2} - \ln 4 please check

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

\frac{2}{x} = - x + 3

x^{2} - 3 x + 2 = 0

x = 1 o r 2

p o i n t o f i n t e r s e c t i n g (1, 2), (2, 1)

\int_{1}^{2} \frac{2}{x} + x - 3

2 l o g 2 + \frac{3}{2} - 3 =∣ 2 l o g 2 - \frac{3}{2} ∣= \frac{3}{2} - 2 l o g 2