Une primitive de 1 x \frac{1}{x} x 1 sur [ ] 0 ; + ∞ [ ] \left[\right]0;+\infty\left[\right] [ ] 0 ; + ∞ [ ] est

x ⟶ ln ⁡ ( x ) x\longrightarrow\ln\left(x\right) x ⟶ ln ( x )

x ⟶ − 1 x ² x\longrightarrow-\frac{1}{x²} x ⟶ − x ² 1

x ⟶ ln ⁡ ( − x ) x\longrightarrow\ln\left(-x\right) x ⟶ ln ( − x )

Une primitive de x ⟶ 1 x x\longrightarrow\ \frac{1}{\sqrt{x}} x ⟶ x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1 sur ∣ 0 ; + ∞ ∣ \left|0;+\infty\right| ∣ 0 ; + ∞ ∣ est

x ⟶ 2 x x\longrightarrow2\sqrt{x} x ⟶ 2 x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x ⟶ x x\longrightarrow\sqrt{x} x ⟶ x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x ⟶ − 1 2 x x x\longrightarrow-\ \frac{1}{2x\sqrt{x}} x ⟶ − 2 x x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1

f d e ˊ f i n i e p a r f ( x ) = − cos ⁡ ( x ) f\ définie\ par\ f\left(x\right)=-\cos\left(x\right) f d e ˊ f i n i e p a r f ( x ) = − cos ( x ) Une de ses primitive est

F ( x ) = − sin ⁡ x F\left(x\right)=-\sin x F ( x ) = − sin x

F ( x ) = sin ⁡ ( − x ) F\left(x\right)=\sin\left(-x\right) F ( x ) = sin ( − x )

F ( x ) = sin ⁡ x F\left(x\right)=\sin x F ( x ) = sin x

F ( x ) = − sin ⁡ ( − x ) F\left(x\right)=-\sin\left(-x\right) F ( x ) = − sin ( − x )

f d e ˊ f i n i e p a r f ( x ) = sin ⁡ ( 2 x + 7 ) f\ définie\ par\ f\left(x\right)=\sin\left(2x+7\right) f d e ˊ f i n i e p a r f ( x ) = sin ( 2 x + 7 ) Une primitive est

F ( x ) = − 1 2 cos ⁡ ( 2 x + 7 ) F\left(x\right)=-\frac{1}{2}\cos\left(2x+7\right) F ( x ) = − 2 1 cos ( 2 x + 7 )

F ( x ) = 2 cos ⁡ ( 2 x + 7 ) F\left(x\right)=2\cos\left(2x+7\right) F ( x ) = 2 cos ( 2 x + 7 )

F ( x ) = − 2 cos ⁡ ( 2 x + 7 ) F\left(x\right)=-2\cos\left(2x+7\right) F ( x ) = − 2 cos ( 2 x + 7 )

F ( x ) = 1 2 cos ⁡ ( 2 x + 7 ) F\left(x\right)=\frac{1}{2}\cos\left(2x+7\right) F ( x ) = 2 1 cos ( 2 x + 7 )

f d e ˊ f i n i e p a r f ( x ) = e x ² f\ définie\ par\ f\left(x\right)=e^{x²} f d e ˊ f i n i e p a r f ( x ) = e x ² Une primitive est

F ( x ) = e x ² F\left(x\right)=e^{x²} F ( x ) = e x ²

F ( x ) = 2 x e x ² F\left(x\right)=2xe^{x²} F ( x ) = 2 x e x ²

F ( x ) = 1 2 x e x ² F\left(x\right)=\frac{1}{2}xe^{x²} F ( x ) = 2 1 x e x ²

f d e ˊ f i n i e p a r f ( x ) = sin ⁡ x 1 − cos ⁡ x f\ définie\ par\ f\left(x\right)=\frac{\sin x}{1-\cos x} f d e ˊ f i n i e p a r f ( x ) = 1 − cos x sin x Une primitive est

F ( x ) = ln ⁡ ( 1 − cos ⁡ x ) F\left(x\right)=\ln\left(1-\cos x\right) F ( x ) = ln ( 1 − cos x )

F ( x ) = 1 − cos ⁡ x F\left(x\right)=\sqrt{1-\cos x} F ( x ) = 1 − cos x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

F ( x ) = 1 ( 1 − cos ⁡ x ) ² F\left(x\right)=\frac{1}{\left(1-\cos x\right)²} F ( x ) = ( 1 − cos x ) ² 1

F ( x ) = 1 1 − cos ⁡ ( x ) F\left(x\right)=\frac{1}{1-\cos\left(x\right)} F ( x ) = 1 − cos ( x ) 1

f d e ˊ f i n i e p a r f ( x ) = − 1 x f\ définie\ par\ f\left(x\right)=-\frac{1}{x} f d e ˊ f i n i e p a r f ( x ) = − x 1 Une primitive est

F ( x ) = − ln ⁡ ( − x ) F\left(x\right)=-\ln\left(-x\right) F ( x ) = − ln ( − x )

F ( x ) = ln ⁡ ( x ) F\left(x\right)=\ln\left(x\right) F ( x ) = ln ( x )

F ( x ) = 1 x ² F\left(x\right)=\frac{1}{x²} F ( x ) = x ² 1

∫ a b f ( x ) d x = \int_a^bf\left(x\right)dx= ∫ a b f ( x ) d x =

− ∫ b a f ( x ) d x -\int_b^af\left(x\right)dx − ∫ b a f ( x ) d x

∫ b a ( − f ) ( t ) d t \int_b^a\left(-f\right)\left(t\right)dt ∫ b a ( − f ) ( t ) d t

∫ b a f ( x ) d x \int_b^af\left(x\right)dx ∫ b a f ( x ) d x

− ∫ a b f ( t ) d t -\int_a^bf\left(t\right)dt − ∫ a b f ( t ) d t

Chapitre 13 intégration

Quiz

•

Mathematics

•

12th Grade

•

Practice Problem

•

Hard

valerie Doumergue

Used 8+ times

FREE Resource

14 questions

Show all answers

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Une primitive de $\frac{1}{x}$ sur $\left[\right]0;+\infty\left[\right]$ est

$x\longrightarrow\ln\left(x\right)$

on ne sait pas

$x\longrightarrow-\frac{1}{x²}$

$x\longrightarrow\ln\left(-x\right)$

MULTIPLE SELECT QUESTION

1 min • 1 pt

Une primitive de $x\longrightarrow\ \frac{1}{\sqrt{x}}$ sur $\left|0;+\infty\right|$ est

$x\longrightarrow\sqrt{x}$

$x\longrightarrow-\ \frac{1}{2x\sqrt{x}}$

$x\longrightarrow2\sqrt{x}$

On ne sait pas

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Une primitive de $x\longrightarrow\ \frac{1}{x^3}$ sur $\left|-\infty;0\right|$ est

$x\longrightarrow\ \frac{1}{2x²}$

$x\longrightarrow\ -\ \frac{1}{2x²}$

$x\longrightarrow\ \frac{1}{3x²}$

$x\longrightarrow\ -\ \frac{1}{3x²}$

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Une primitive de $x\longrightarrow x^8$ est

$F\left(x\right)=8x^7$

$F\left(x\right)=9x^7$

$F\left(x\right)=\frac{x^9}{9}$

$F\left(x\right)=\frac{x^9}{8}$

MULTIPLE SELECT QUESTION

1 min • 1 pt

$f\ définie\ par\ f\left(x\right)=-\cos\left(x\right)$

Une de ses primitive est

$F\left(x\right)=\sin x$

$F\left(x\right)=-\sin x$

$F\left(x\right)=\sin\left(-x\right)$

$F\left(x\right)=-\sin\left(-x\right)$

MULTIPLE SELECT QUESTION

1 min • 1 pt

$f\ définie\ par\ f\left(x\right)=\sin\left(2x+7\right)$

Une primitive est

$F\left(x\right)=2\cos\left(2x+7\right)$

$F\left(x\right)=-2\cos\left(2x+7\right)$

$F\left(x\right)=\frac{1}{2}\cos\left(2x+7\right)$

$F\left(x\right)=-\frac{1}{2}\cos\left(2x+7\right)$

MULTIPLE SELECT QUESTION

1 min • 1 pt

$f\ définie\ par\ f\left(x\right)=e^{x²}$

Une primitive est

$F\left(x\right)=e^{x²}$

$F\left(x\right)=2xe^{x²}$

$F\left(x\right)=\frac{1}{2}xe^{x²}$

On ne sait pas

MULTIPLE SELECT QUESTION

1 min • 1 pt

$f\ définie\ par\ f\left(x\right)=\frac{\sin x}{1-\cos x}$

Une primitive est

$F\left(x\right)=\ln\left(1-\cos x\right)$

$F\left(x\right)=\sqrt{1-\cos x}$

$F\left(x\right)=\frac{1}{\left(1-\cos x\right)²}$

$F\left(x\right)=\frac{1}{1-\cos\left(x\right)}$

MULTIPLE SELECT QUESTION

1 min • 1 pt

$f\ définie\ par\ f\left(x\right)=-\frac{1}{x}$

Une primitive est

$F\left(x\right)=\ln\left(x\right)$

$F\left(x\right)=-\ln\left(-x\right)$

$F\left(x\right)=\frac{1}{x²}$

On ne sait pas

10.

MULTIPLE SELECT QUESTION

1 min • 1 pt

$\int_a^bf\left(x\right)dx=$

$\int_b^af\left(x\right)dx$

$-\int_b^af\left(x\right)dx$

$-\int_a^bf\left(t\right)dt$

$\int_b^a\left(-f\right)\left(t\right)dt$

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Chapitre 13 intégration

14 questions

Une primitive de 1x\frac{1}{x}x1​ sur []0;+∞[]\left[\right]0;+\infty\left[\right][]0;+∞[] est

Une primitive de x⟶ 1xx\longrightarrow\ \frac{1}{\sqrt{x}}x⟶ x​1​ sur ∣0;+∞∣\left|0;+\infty\right|∣0;+∞∣ est

Une primitive de x⟶ 1x3x\longrightarrow\ \frac{1}{x^3}x⟶ x31​ sur ∣−∞;0∣\left|-\infty;0\right|∣−∞;0∣ est

Une primitive de x⟶x8x\longrightarrow x^8x⟶x8 est

f deˊfinie par f(x)=−cos⁡(x)f\ définie\ par\ f\left(x\right)=-\cos\left(x\right)f deˊfinie par f(x)=−cos(x) Une de ses primitive est

f deˊfinie par f(x)=sin⁡(2x+7)f\ définie\ par\ f\left(x\right)=\sin\left(2x+7\right)f deˊfinie par f(x)=sin(2x+7) Une primitive est

f deˊfinie par f(x)=ex²f\ définie\ par\ f\left(x\right)=e^{x²}f deˊfinie par f(x)=ex² Une primitive est

f deˊfinie par f(x)=sin⁡x1−cos⁡xf\ définie\ par\ f\left(x\right)=\frac{\sin x}{1-\cos x}f deˊfinie par f(x)=1−cosxsinx​ Une primitive est

f deˊfinie par f(x)=−1xf\ définie\ par\ f\left(x\right)=-\frac{1}{x}f deˊfinie par f(x)=−x1​ Une primitive est

∫abf(x)dx=\int_a^bf\left(x\right)dx=∫ab​f(x)dx=

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Une primitive de $\frac{1}{x}$ sur $\left[\right]0;+\infty\left[\right]$ est

Une primitive de $x\longrightarrow\ \frac{1}{\sqrt{x}}$ sur $\left|0;+\infty\right|$ est

Une primitive de $x\longrightarrow\ \frac{1}{x^3}$ sur $\left|-\infty;0\right|$ est

Une primitive de $x\longrightarrow x^8$ est

$f\ définie\ par\ f\left(x\right)=-\cos\left(x\right)$

Une de ses primitive est

$f\ définie\ par\ f\left(x\right)=\sin\left(2x+7\right)$

Une primitive est

$f\ définie\ par\ f\left(x\right)=e^{x²}$

Une primitive est

$f\ définie\ par\ f\left(x\right)=\frac{\sin x}{1-\cos x}$

Une primitive est

$f\ définie\ par\ f\left(x\right)=-\frac{1}{x}$

Une primitive est

$\int_a^bf\left(x\right)dx=$