Hitunglah :

Jawab:

∫ 4x sin x dx

parsial ,  dgn tanzalin

4x   sin x

4      -cos x

0      -sin x

= 4x (-cos x) – (4)(-sin x) + c

= – 4x cos x +  4 sin x +c

b)  f(x)=  3x² – 2x  +5

a= 3,  b= – 2,  c= 5

nilai 2a+  3b+ 4c=

= 2(3) + 3(-2) + 4(5)

= 6 – 6 + 20

= 20

Penjelasan dengan langkah-langkah:

a.

∫ 4x sinx dx

rumus integral parsial

∫ udv = u.v – ∫ v.du

u = 4x

du/dx = 4

du = 4dx

dv = sinx

v = -cos x

u.v = 4x(-cosx)

u.v = -4x.cosx

∫ vdu

= ∫ -cosx 4dx

= ∫ -4cosx dx

= – 4sinx

∫ 4x sinx dx

= – 4cosx – (-4sinx)

= – 4x. cosx + 4sinx + c

b.

f(x) = 3x² – 2x + 5

a = 3 ; b = – 2 ; c = 5

nilai dari :

2a + 3b + 4c

= 2(3) + 3(-2) + 4(5)

= 6 – 6 + 20

= 20