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Bộ 23 đề thi thử THPTQG năm 2018 - Môn Toán - Gv Đặng Việt Đông - Lovebook - Có lời giải chi tiết

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1 1 1 1<br />

2 2 3 2 2 2 2 2<br />

( ) ( ) ( ) ( )<br />

<br />

S = x x + 1dx = x + x d x + 1 = x + x x + 1 − x + 1. 3x + 1 dx<br />

0 0 0 0<br />

1<br />

2<br />

2 2 -3 - 1<br />

= S x + dx<br />

<br />

0<br />

Đặt x = tan x a = 3, b = 2, c = 8<br />

Câu 49: Đáp án A.<br />

Đặt<br />

( ) '( )<br />

u = f x du = f x dx<br />

<br />

dv = sin xdx v = −cos<br />

x<br />

<br />

<br />

2 2 2<br />

2<br />

( ) ( ) ( ) ( ) ( )<br />

<br />

f x .sin xdx = − f x .cos x + f ' x .cos xdx 1 = f 0 + f ' x .cos xdx<br />

0 0 0<br />

0<br />

<br />

2<br />

<br />

0<br />

( )<br />

f ' x .cos xdx = 0<br />

Đặt<br />

( ) ''( )<br />

u = f ' x du = f x dx<br />

<br />

<br />

dv = cos xdx v = sin x<br />

<br />

<br />

<br />

2 2<br />

2<br />

( ) ( ) ( )<br />

<br />

0 = f ' x .cos xdx = f ' x .sin x − f '' x .sin xdx<br />

0 0<br />

0<br />

<br />

0 = f ' −1 f ' = 1<br />

2 2<br />

Câu 50: Đáp án A.<br />

( ) ( ) ( ) ( )<br />

g x = 6 f x + x g ' x = 6 f ' x + 3x<br />

3 2<br />

( ) ( ) ( )<br />

g '' x = 6. f '' x + 6x = 6 f '' x + x<br />

x<br />

=−3<br />

<br />

x = 4<br />

g ''( x) = 0 f ''( x)<br />

= −x<br />

<br />

x =<br />

3<br />

x<br />

= 1<br />

1 3 4<br />

<br />

Theo hình vẽ ta có: − − ''( ) ''( ) + − − ''( )<br />

x f x dx f x x dx x f x <br />

dx<br />

−3 1 3<br />

−x x −x<br />

<br />

− f '( x) f '( x) f '( x)<br />

2<br />

+ −<br />

2<br />

<br />

2<br />

<br />

<br />

2 1 2 3 2<br />

4<br />

−3 1<br />

3<br />

1 3<br />

4<br />

( ) ( ) ( )<br />

−g ' x g ' x − g ' x<br />

−3 1<br />

3

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