7/23/2019 Integral Alv

1/2

1)

Rcos1 xdx

= cos1 x

cos = x sin d = dxR

cos1 xdx=R

( sin d)=

R sin d u= dv= sin d

du= d v= cos =

R sin d = cos +

Rcos d

= cos + sin = x cos1 x+ sin

cos1 x

4)R10

xpx+1

dx u= x+ 1 du= dxx= u 1

R u1pudu =

R upudu R

du

pu

=R

u1 u 12 du R

u1

2 du

=R

u1

2 du u1

2

1

2

= u3

2

3

2

u1

2

1

2

=h2

3(x+ 1)

3

2 2 (x+ 1)1

2

i10

= 23

(1 + 1)3

22 (1 + 1)1

2 23

(0 + 1)3

2 +2 (0 + 1)1

2 = 43 2

3

p2 =

0:39052=

***************6)R

xp

8 xdxu= 8 x x= 8 udu= dxR

xp

8 xdx=R

(8 u)p

u (du) = 8R

u1

2 du +R

u3

2 du= 25

u5

2 163

u3

2 =2

5(8 x)

5

2 163

(8 x)3

2

*****************7)R

2x+19

x2+7x+10dx

=R

2x+7

x2+7x+10dx+

R 12

x2+7x+10dx

u= x2 + 7x+ 10du= (2x+ 7) dx9)f(x) = x2 + 3 [2; 3]Rb

af(x) dx=

R32

x2 + 3

dx=

1

3x3 + 3x

32

= 1

3(3)3 + 3 (3)

1

3(

2)3 + 3 (

2)= 1

3 27 + 9

83 6

= 9 + 9 + 8

3+ 6 = 80

3

10)g(x) = 4xf(x) = g(x) = 4x= x3 +x2 + 16x

x3 x2 16x+ 4x= 0

1

7/23/2019 Integral Alv

2/2

x3 x2 12x= 0x x

2

x

12= 0x (x 4) (x+ 3) = 0

es igual es:x= 0x= 4x= 3f(x) = x3 +x2 + 16x= x

x2 x 16

= x

x2 x 16

v=R43

x3 +x2 + 16x

dx

R434xdx

v=x4

4 + x

3

3 + 8x2

43

2x243 =

343

12

2