ĐGTD ĐH Bách khoa - Tư duy Toán học - Tích phân (tích phân từng phần)

$I=f\left(x\right).g\text{'}\left(x\right)|{}_a^b-\underset{a}{\overset{b}{\int }}f\text{'}\left(x\right).g\left(x\right)dx$

$I=f\left(x\right).g\left(x\right)|{}_a^b-\underset{a}{\overset{b}{\int }}f\left(x\right).g\left(x\right)dx$

$I=f\left(x\right).g\left(x\right)|{}_a^b-\underset{a}{\overset{b}{\int }}f\text{'}\left(x\right).g\left(x\right)dx$

$I=f\left(x\right).g\text{'}\left(x\right)|{}_a^b-\underset{a}{\overset{b}{\int }}f\left(x\right).g\text{'}\left(x\right)dx$

I = 2

I = 1

I = 3

I = -1

$I=x^2\sin x{|}_0^{\pi }-\underset{0}{\overset{\pi }{}}x\sin xdx$

$I=x^2\sin x{|}_0^{\pi }+2\underset{0}{\overset{\pi }{}}x\sin xdx$

$I=x^2\sin x{|}_0^{\pi }-2\underset{0}{\overset{\pi }{}}x\sin xdx$

I = -12

I = 8

I = 12

I = -8

$f\left(x\right)=-\frac{{\pi }^x}{\ln \pi }$

$f\left(x\right)=\frac{{\pi }^x}{\ln \pi }$

$f\left(x\right)={\pi }^x.\ln \pi$

$f\left(x\right)=-{\pi }^x.\ln \pi$

I = 0

I = -1

I = 1

I = 2

8

9

24

36

$\frac{e^2-1}{2}$

$\frac{e^2+1}{2}$

$\frac{e^2-3}{4}$

$\frac{e^2-3}{2}$

$I=\frac{1}{2}$

$I=\frac{3e^2+1}{4}$

$I=\frac{e^2+1}{4}$

$I=\frac{e^2-1}{4}$

$I=-\frac{\ln 2^{1000}}{1+2^{1000}}+\ln \frac{2^{1001}}{1+2^{1000}}$

$I=-\frac{1000\ln 2}{1+2^{1000}}+\ln \frac{2^{1000}}{1+2^{1000}}$

$I=\frac{\ln 2^{1000}}{1+2^{1000}}-1001\ln \frac{2}{1+2^{1000}}$

$I=\frac{1000\ln 2}{1+2^{1000}}-\ln \frac{2^{1000}}{1+2^{1000}}$

$-\frac{1}{13}$

$-\frac{5}{13}$

$\frac{5}{13}$

$\frac{1}{13}$

$a+b+c=1$

$a-b+c=0$

$a+2b+c=0$

$2a+b+c=-1$

$b+c=127075$

$b+c=127073$

$b+c=127072$

$b+c=127071$

2017

2018

4034

4036

S = 0

S = 1

$S=\frac{1}{2}$

$S=\frac{3}{8}$

$\frac{1}{2}$

$\frac{1}{4}$

1

0

$a-b=-1$

$a+b=1$

$a+b=2$

$a-b=0$

1

$\frac{5}{2}$

$\frac{1}{3}$

$-\frac{1}{3}$

$\frac{32}{15}$

$\frac{86}{15}$

$\frac{-11}{15}$

$\frac{16}{15}$

-30

-50

15

25

1

-1

-2

2

23

5

20

27

2

7

4

5

bằng 12.

bằng 10.

bằng 8.

bằng 6.

250

251

133

221

5+8ln2

3-8ln2

5-8ln2

7-8ln2

3(1-e)

3e

0

3(e-1)