Actually Welcome to the Concept of the Angles.
11) Vertically Opposite Angles, 6x= 30 , thus x= 5
12) Adjacent Angles, 4+5x+x+2 = 180
= 6+6x= 180 => 1+x= 30 , x= 29
13) Right Angle, 2x+1+x+2=90 ==> 3x+3=90 => x+1= 30
=> x=29
14) Right Angle, 3x+1+4+2x = 5x+5= 90 ==> x+1 = 18
=> x=17
15)Vertically Opposite Angles are same,
y+23= 63 , thus y= 63-23 ==> y= 40
2x-17 = 234 ( remaining angle after subtraction of 63 for two times)
2x= 251 , thus x= 125.5
16)Linear pair, 47-2x+x^2+32 = 180
=> 79-2x+x^2= 180
= x^2-2x = 101
=x(x-2) = 101
17)
Answer:
sin2x +
x + c
Step-by-step explanation:
using the trigonometric identity
• cos² x = (cos2x + 1) and
∫cos ax = sin ax
hence
∫(1 - (cos2x + 1)dx
= ∫(1 - cos2x -
)dx
= ∫( -
cos2x)dx
= x -
sin2x + c
where c is the constant of integration