`(dy)/(dx)=e^(-2y)andy=0w h e nx=5,t h e v a l u e o fxf o ry=3`

IfI_n=int_0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

IfI_n=int_0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

IfI_n=int_x^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

IfI=int(dx)/(secx+cos e cx),t h e nIe q u a l s

I fx+1/x=2,t h e p r i n c i p a l v a l u e o f sin^(-1)x is

Ifint_(pi/3)^xsqrt((3-sin^2t))dt+int_0^ycostdt=0,t h e ne v a l u a t e(dy)/(dx)

Ifint_(pi/3)^xsqrt((3-sin^2t))dt+int_0^ycostdt=0,t h e ne v a l u a t e(dy)/(dx)

Solution of (dy)/(dx)+2x y=y is (a) ( b ) (c) y=c (d) e^( e ) (f) x-( g ) x^((( h )2( i ))( j ) (k))( l ) (m) (n) (b) ( o ) (p) y=c( q ) e^( r ) (s) (t) x^((( u )2( v ))( w )-x (x))( y ) (z) (aa) (c) ( d ) (e) y=c( f ) e^(( g ) x (h))( i ) (j) (k) (d) ( l ) (m) y=c (n) e^( o ) (p)-( q ) x^((( r )2( s ))( t ) (u))( v ) (w) (x)

Show that f(x)={(x-|x|)/(2),2 w h e nx!=0i sd i s con t inuou sa tx=0dotw h e nx=0

Solve the differential equation (dy)/(dx)=(2x(logx+1))/(siny+ycosy) , given that y=0,w h e nx=1.