<span> ∫ [ln(√t) / t] dx
let √t = u
t= u² → dx = 2u du
substitute in the integral
∫ [ln(√t) / t] dx = ∫ (ln u / u²) 2u du = ∫ (ln u / u²) 2u du = 2 ∫ (ln u / u) du
let ln u = x → d (ln u) = dx→ (1/u)du = dx
substituting again
2 ∫ (ln u / u) du = 2 ∫ x dx= 2 x²/ 2 = x² + c which,
substituting ln² u + c
as of the first
substitution ln²(√t) + c
it concludes that
∫ [ln(√t) / t] dx = ln²(√t) + c
hope it helps
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The easiest way to do this is to work out f(-2) first, =-3(-2)+4=10, then find g(-2)=(-2)²=4.
(g*f)(-2)=4×10=40.
However, if g*f means g of f the answer is different, because having worked out that f(-2)=10 we put this result into g, so we find g(10)=10²=100.
So you need to determine whether g*f means g(x)×f(x) [answer 40] or g(f(x)) [answer 100] when x=-2.
The simplest form is 4/7 or 0.5174.
Answer:
48
Step-by-step explanation:
using the formula 1/2 b*h
8*12=96
96/2=48
Answer:
8
Step-by-step explanation:
use trig functions
2 sides and 1 angle given
Sides given
- hypotenuse -> x
- opposite side to 30˚ -> 4
Angle
trig function associated with hyp and opp is sin
sin(x) = opp/hyp
substitute
sin 30˚ = 4/x
solve for x
0.5 = 4/x
0.5x = 4
x = 8
