Given-a-function-f-where-f-x-0for-x-R-If-the-area-U-x-y-0-2y-f-x-6-x-2-is-u-and-the-area-V-x-y-0-y-f-x-2-x-0-is-v-then-what-the-value-of-1-2-4x-f-2x-2-8-dx-A-5u-4v-

Question Number 138611 by liberty last updated on 15/Apr/21

G i v e n a f u n c t i o n f w h e r e

f (x) ⩾ 0 f o r \forall x \in R . I f t h e a r e a

U = {(x, y) ∣ 0 ⩽ 2 y ⩽ f (x), - 6 ⩽ x ⩽ - 2}

i s u a n d t h e a r e a V = {(x, y) ∣ 0 ⩽ y ⩽ f (x), - 2 ⩽ x ⩽ 0}

i s v t h e n w h a t t h e v a l u e o f

\underset{1}{\int^{2}} 4 x f (2 x^{2} - 8) d x .

(A) 5 u + 4 v (D) 2 u + v

(B) 4 u + 3 v (E) u + v

(C) 3 u + 2 v

Answered by ajfour last updated on 15/Apr/21

u = \frac{1}{2} \int_{- 6}^{- 2} f (x) d x = \frac{F (- 2) - F (- 6)}{2}

v = \int_{- 2}^{0} f (x) d x = F (0) - F (- 2)

I = \int_{1}^{2} 4 x f (2 x^{2} - 8) d x

l e t 2 x^{2} - 8 = t

\Rightarrow 4 x d x = d t

I = \int_{- 6}^{0} f (x) d x = F (0) - F (- 6)

= 2 u + v (D) .

Answered by tepebea last updated on 16/Apr/21

m a n t a p \dots

Commented by ajfour last updated on 16/Apr/21

w h a t d o e s t h i s m e a n i n E n g l i s h . .

Commented by tepebea last updated on 16/Apr/21

g o o d j o b o r {t h a t}^{'} s g r e a t

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