Integrals Ex 7.1 Class 12

[Pages:124]Integrals Ex 7.1 Class 12

Ex 7.1 Class 12 Maths Question 1. sin 2x Solution:

Ex 7.1 Class 12 Maths Question 2. cos 3x Solution:

Ex 7.1 Class 12 Maths Question 3.

e2x

Solution:

Ex 7.1 Class 12 Maths Question 4. (ax + c)? Solution:

Ex 7.1 Class 12 Maths Question 5.

sin 2x - 4e 3x

Ex 7.1 Class 12 Maths Solution:

Find the following integrals in Exercises 6 to 20 :

Ex 7.1 Class 12 Maths Question 6.

(4e3x + 1) dx

Solution:

Ex 7.1 Class 12 Maths Question 7.

x2

(1 -

1 x2

)

dx

Solution:

Ex 7.1 Class 12 Maths Question 8.

(ax 2 + bx + c)dx

Solution:

Ex 7.1 Class 12 Maths Question 9.

(2x2 + ex ) dx

Solution:

Ex 7.1 Class 12 Maths Question 10.

[-x -

1 x

2

]

dx

Solution:

Ex 7.1 Class 12 Maths Question 11.

Solxu3t+iox5nx2:2-4dx

Ex 7.1 Class 12 Maths Question 12.

x3+3x+4 dx

x

Solution:

Ex 7.1 Class 12 Maths Question 13.

x

3

-x 2 +x-1 x-1

dx

Solution:

Ex(71.1-Clxa)ss12-xMdxaths Question 14.

Solution:

Ex 7.1 Class 12 Maths Question 15.

-x (3x2 + 2x + 3) dx

Solution:

Ex 7.1 Class 12 Maths Question 16.

(2x - 3cosx + ex )dx

Solution:

Ex 7.1 Class 12 Maths Question 17.

(2x2 - 3sinx + 5-x ) dx

Solution:

Ex 7.1 Class 12 Maths Question 18.

secx(secx + tanx)dx

Solution: Ex 7.1 Class 12 Maths Question 19.

Solcuostesiceoc2nx2:x dx

Ex 7.1 Class 12 Maths Question 20.

Sol2u-ctio3ossn2inx:x dx

Ex 7.1 Class 12 Maths Question 21.

The antiderivative (-x +

1 x

)

equals

(a)

1 3

x

1 3

+

2x

1 2

+c

(b) (c)

2 3

x

2 3

\frac {

+2 }{12

x

3

2

}

+c

{ x }^{

\frac

{

3

}{

2

}

}+{

2x

}^{

\frac

{

1

}{

2

}

}+c

2 3

x

3 2

+

2x

1 2

+c

(Sdo)lu32tixon32:

+

1 2

x

1 2

+c

Ex 7.1 Class 12 Maths Question 22.

If

d dx

(a) x

(b) {

f

4

x

(x) = 4x3 -

+1

}^{x33

-

129 8

}+\frac {

3 such that f(2)=0 then f(x) is

x4

1 }{ { x }^{ 4 } } +\frac { 129 }{

8

}

x3

+

1 x4

(c) x4 +

(d) x3 +

Solution:

+

1 x13 x4

129

8

+

129 8

-

129 8

Integrals Ex 7.2 Class 12

Ex 7.2 Class 12 Maths Question 1.

2x 1+x 2

Solution:

Ex 7.2 Class 12 Maths Question 2.

(logx)2 x

Solution:

Ex 7.2 Class 12 Maths Question 3.

1 x+xlogx

Solution:

Ex 7.2 Class 12 Maths Question 4. sinx sin(cosx) Solution:

Ex 7.2 Class 12 Maths Question 5. sin(ax+b) cos(ax+b) Solution:

Ex-a7-x.2-+C--lbass 12 Maths Question 6.

Solution:

Exx7-x.2-+C--l2ass 12 Maths Question 7.

Solution:

Exx7-.12-+C-l-a2s-xs-122 Maths Question 8.

Solution:

E(4xx7.+2 C2la)ss 1-x2-2M-+-at-xh-s+Q--u1estion 9.

Solution:

Ex 7.2 Class 12 Maths Question 10.

1 x-x

Solution:

Ex 7.2 Class 12 Maths Question 11.

x ,x> 0

x+4

Solution:

Ex 7.2 Class 12 Maths Question 12.

(x3

-

1)

1 3

.

x5

Solution:

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