Какая из данных функций не является первообразной для функции f ( x ) = C o s 3 x f\left(x\right)=Cos3x f ( x ) = C o s 3 x

F ( x ) = 2 + 1 3 S i n 3 x F\left(x\right)=2+\frac{1}{3}Sin3x F ( x ) = 2 + 3 1 S i n 3 x

F ( x ) = 1 3 S i n 3 x F\left(x\right)=\frac{1}{3}Sin3x F ( x ) = 3 1 S i n 3 x

F ( x ) = 4 + 1 3 S i n 3 x F\left(x\right)=4+\frac{1}{3}Sin3x F ( x ) = 4 + 3 1 S i n 3 x

F ( x ) = 2 − 1 3 S i n 3 x F\left(x\right)=2-\frac{1}{3}Sin3x F ( x ) = 2 − 3 1 S i n 3 x

Какая из данных функций не является первообразной для функции f ( x ) = S i n 2 x f\left(x\right)=Sin2x f ( x ) = S i n 2 x

F ( x ) = 4 − 1 2 C o s 2 x F\left(x\right)=4-\frac{1}{2}Cos2x F ( x ) = 4 − 2 1 C o s 2 x

F ( x ) = 2 − 1 2 C o s 2 x F\left(x\right)=2-\frac{1}{2}Cos2x F ( x ) = 2 − 2 1 C o s 2 x

F ( x ) = − 1 2 C o s 2 x F\left(x\right)=-\frac{1}{2}Cos2x F ( x ) = − 2 1 C o s 2 x

F ( x ) = − 2 C o s 2 x F\left(x\right)=-2Cos2x F ( x ) = − 2 C o s 2 x

Найдите первообразную для функции f ( x ) = 3 x f\left(x\right)=3^x f ( x ) = 3 x

F ( x ) = 3 x ln ⁡ 3 + C F\left(x\right)=\frac{3^x}{\ln3}+C F ( x ) = ln 3 3 x + C

F ( x ) = 3 x + 1 x + 1 + C F\left(x\right)=\frac{3^{x+1}}{x+1}+C F ( x ) = x + 1 3 x + 1 + C

F ( x ) = 3 x ln ⁡ 3 + C F\left(x\right)=3^x\ln3+C F ( x ) = 3 x ln 3 + C

F ( x ) = 1 3 x + C F\left(x\right)=\frac{1}{3}x+C F ( x ) = 3 1 x + C

Найдите первообразную для функции f ( x ) = x − 5 f\left(x\right)=\sqrt{x-5} f ( x ) = x − 5 <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 ) = 2 3 ( x − 5 ) 3 2 + C F\left(x\right)=\frac{2}{3}\left(x-5\right)^{\frac{3}{2}}+C F ( x ) = 3 2 ( x − 5 ) 2 3 + C

F ( x ) = 1 5 x − 5 + C F\left(x\right)=\frac{1}{5\sqrt{x-5}}+C F ( x ) = 5 x − 5 <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 + C

F ( x ) = 2 ( x − 5 ) 1 2 F\left(x\right)=\frac{2}{\left(x-5\right)^{\frac{1}{2}}} F ( x ) = ( x − 5 ) 2 1 2

F ( x ) = 1 5 x − 5 + C F\left(x\right)=\frac{1}{5}\sqrt{x-5}+C F ( x ) = 5 1 x − 5 <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"> + C

Найдите неопределенный интеграл ∫ x 2 3 d x \int_{ }^{ }x^{\frac{2}{3}}dx ∫ x 3 2 d x

3 x 5 3 5 + C \frac{3x^{\frac{5}{3}}}{5}+C 5 3 x 3 5 + C

3 5 x 5 3 + C \frac{3}{5}x^{\frac{5}{3}}+C 5 3 x 3 5 + C

3 5 x 3 5 + C \frac{3}{5}x^{\frac{3}{5}}+C 5 3 x 5 3 + C

3 x 3 5 5 + C \frac{3x^{\frac{3}{5}}}{5}+C 5 3 x 5 3 + C

Найдите неопределенный интеграл ∫ ( 5 x + 1 − e 5 x − 1 ) d x \int_{ }^{ }\left(\frac{5}{x+1}-e^{5x-1}\right)dx ∫ ( x + 1 5 − e 5 x − 1 ) d x

5 ln ⁡ ∣ x + 1 ∣ − 1 5 e 5 x − 1 + C 5\ln\left|x+1\right|-\frac{1}{5}e^{5x-1}+C 5 ln ∣ x + 1 ∣ − 5 1 e 5 x − 1 + C

1 5 ln ⁡ ∣ x ∣ − 5 e x + C \frac{1}{5}\ln\left|x\right|-5e^x+C 5 1 ln ∣ x ∣ − 5 e x + C

5 ln ⁡ ∣ x ∣ − 1 5 e x + C 5\ln\left|x\right|-\frac{1}{5}e^x+C 5 ln ∣ x ∣ − 5 1 e x + C

1 5 ln ⁡ ∣ x + 1 ∣ − 5 e 5 x − 1 + C \frac{1}{5}\ln\left|x+1\right|-5e^{5x-1}+C 5 1 ln ∣ x + 1 ∣ − 5 e 5 x − 1 + C

Найдите неопределенный интеграл ∫ ( S i n 5 x C o s 4 x + S i n 4 x C o s 5 x ) d x \int_{ }^{ }\left(Sin5x\ Cos4x\ +\ Sin4x\ Cos5x\right)dx ∫ ( S i n 5 x C o s 4 x + S i n 4 x C o s 5 x ) d x

− 1 9 C o s 9 x + C -\frac{1}{9}Cos9x+C − 9 1 C o s 9 x + C

− 1 9 S i n 9 x + C -\frac{1}{9}Sin9x+C − 9 1 S i n 9 x + C

1 20 C o s 5 x S i n 4 x − 1 20 C o s 4 x S i n 5 x + C \frac{1}{20}Cos5xSin4x-\frac{1}{20}Cos4xSin5x+C 2 0 1 C o s 5 x S i n 4 x − 2 0 1 C o s 4 x S i n 5 x + C

− 1 5 C o s 5 x 1 4 S i n 4 x − 1 4 C o s 4 x 1 5 S i n 5 x + C -\frac{1}{5}Cos5x\ \frac{1}{4}Sin4x-\frac{1}{4}Cos4x\ \frac{1}{5}Sin5x+C − 5 1 C o s 5 x 4 1 S i n 4 x − 4 1 C o s 4 x 5 1 S i n 5 x + C

Первообразная и интеграл

Authored by Людмила Новосельцева

Mathematics

5th Grade

Used 153+ times

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Выберите первообразную для функции $f\left(x\right)=4x-1$

$F\left(x\right)=16x^2-x$

$F\left(x\right)=2x^2$

$F\left(x\right)=2x^2-x+1$

$F\left(x\right)=16x^2$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Выберите первообразную для функции $f\left(x\right)=2-x$

$F\left(x\right)=2x-2x^2$

$F\left(x\right)=-0,5x^2+2x+1$

$F\left(x\right)=2-x^2$

$F\left(x\right)=-0,5x^2$

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Какая из данных функций не является первообразной для функции $f\left(x\right)=Cos3x$

$F\left(x\right)=2+\frac{1}{3}Sin3x$

$F\left(x\right)=\frac{1}{3}Sin3x$

$F\left(x\right)=2-\frac{1}{3}Sin3x$

$F\left(x\right)=4+\frac{1}{3}Sin3x$

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Какая из данных функций не является первообразной для функции $f\left(x\right)=Sin2x$

$F\left(x\right)=-\frac{1}{2}Cos2x$

$F\left(x\right)=2-\frac{1}{2}Cos2x$

$F\left(x\right)=-2Cos2x$

$F\left(x\right)=4-\frac{1}{2}Cos2x$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Найдите общий вид первообразных для функции $f\left(x\right)=-5$

F(x) = - 5x+C

F(x) = - 5x

F(x) = - 5 + C

F(x) = 5x + C

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Найдите первообразную для функции $f\left(x\right)=3^x$

$F\left(x\right)=\frac{3^{x+1}}{x+1}+C$

$F\left(x\right)=3^x\ln3+C$

$F\left(x\right)=\frac{1}{3}x+C$

$F\left(x\right)=\frac{3^x}{\ln3}+C$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Найдите первообразную для функции $f\left(x\right)=\sqrt{x-5}$

$F\left(x\right)=\frac{2}{3}\left(x-5\right)^{\frac{3}{2}}+C$

$F\left(x\right)=\frac{1}{5\sqrt{x-5}}+C$

$F\left(x\right)=\frac{2}{\left(x-5\right)^{\frac{1}{2}}}$

$F\left(x\right)=\frac{1}{5}\sqrt{x-5}+C$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Найдите первообразную для функции $f\left(x\right)=\frac{1}{1+\left(3x\right)^2}$

$F\left(x\right)=3ar\operatorname{ctg}x+C$

$F\left(x\right)=\frac{1}{3}ar\operatorname{ctg}3x+C$

$F\left(x\right)=3ar\operatorname{ctg}3x+C$

$F\left(x\right)=\frac{1}{3}ar\operatorname{ctg}x+C$

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

Найдите неопределенный интеграл $\int_{ }^{ }x^3dx$

$3x^2+C$

$\frac{x^2}{2}+C$

$\frac{x^4}{4}+C$

$\frac{3^x}{\ln3}+C$

10.

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Найдите неопределенный интеграл $\int_{ }^{ }x^{\frac{2}{3}}dx$

$\frac{3}{5}x^{\frac{5}{3}}+C$

$\frac{3}{5}x^{\frac{3}{5}}+C$

$\frac{3x^{\frac{5}{3}}}{5}+C$

$\frac{3x^{\frac{3}{5}}}{5}+C$

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Первообразная и интеграл

Выберите первообразную для функции f(x)=4x−1f\left(x\right)=4x-1f(x)=4x−1

Выберите первообразную для функции f(x)=2−xf\left(x\right)=2-xf(x)=2−x

Какая из данных функций не является первообразной для функции f(x)=Cos3xf\left(x\right)=Cos3xf(x)=Cos3x

Какая из данных функций не является первообразной для функции f(x)=Sin2xf\left(x\right)=Sin2xf(x)=Sin2x

Найдите общий вид первообразных для функции f(x)=−5f\left(x\right)=-5f(x)=−5

Найдите первообразную для функции f(x)=3xf\left(x\right)=3^xf(x)=3x

Найдите первообразную для функции f(x)=x−5f\left(x\right)=\sqrt{x-5}f(x)=x−5​

Найдите первообразную для функции f(x)=11+(3x)2f\left(x\right)=\frac{1}{1+\left(3x\right)^2}f(x)=1+(3x)21​

Найдите неопределенный интеграл ∫x3dx\int_{ }^{ }x^3dx∫​x3dx

Найдите неопределенный интеграл ∫x23dx\int_{ }^{ }x^{\frac{2}{3}}dx∫​x32​dx

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