Question

Mohon bantuannya kak


Terima Kasih

Answer 1

1) 
a)  ∫ x√(x²+2) dx = (x)/(2x) (2/3)(x²+2)^(3/2) + c
= 1/3(x²+2) √(x²+2) + c

b) ∫4x² .(sin x³)¹/² (cos x³) dx
= (4x². cos x³ / 3x² cos x³ ) (2/3) (sin x³)^3/2 +C
= 4/3 (2/3)  (sin x³) √ (sin x³) +c
= 8/9 (sin x³)√(sin x³) + c

2) y1= x+5
y2 = x² + 3
y1-y2  = 0
-x² + x + 2 = 0 --> -(x-2)(x+1)= 0
x = 2 atau x =-1
Luas  = ₋₁ ²∫ -x² + x + 2 dx = 9/2

3) y = sin x --> x =  sin⁻¹ y
y = cos x --> x = cos⁻¹ y
V = π .₋₁∫¹ (5π/4 - 1/ sin y ) + (1/cos y  - π/4)
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