Penjelasan dengan langkah-langkah:

18.

a. ∫ sin x dx = -cos x + C

b. ∫ 4 sin x dx = -4 cos x + C

c. ∫ 4 -sin x dx = 4 + cos x + C

d. ∫ 2 sin x + 3x² dx = -2 cos x + x³ + C

19.

a. ∫ (cos x + sin x) dx

= sin x - cos x + C

b. ∫ ( 3 cos x - 4 sin x) dx

= 3 sin x + 4 cos x + C

20.

a.[0 ∫ π/6] cos x dx

= sin x | [ 0 π/6 ]

= sin (π/6) - sin (0)

= ½

b. [0∫ π/2] sin x dx

= -cos x | [ 0 π/2]

= -cos (π/2) -(-cos(0)

= 1

c. [0∫ π] (cos x + sin x) dx

= sin x - cos x |[0. π]

= (sin (π) - cos (π)) - (sin (0) - cos (0))

= 2

21.

a. [0∫ π/2] (1+cos x) dx

= x + sin x | [ 0 π/2]

= (π/2-sin (π/2)) - (0 + sin (0)

= π/2 + 1

b. [-π∫ π] (2x+sin x) dx

= x² - cos x | [ -π π ]

= ( (-π²)-cos (-π)) - ((π)²- cos (π))

= 0