integrals ex 7.1 class 12 - fliplearn

Integrals Ex 7.1 Class 12

Ex 7.1 Class 12 Maths Question 1.sin 2xSolution:

Ex 7.1 Class 12 Maths Question 2.cos 3xSolution:

Ex 7.1 Class 12 Maths Question 3.

Solution:

Ex 7.1 Class 12 Maths Question 4.(ax + c)²Solution:


Ex 7.1 Class 12 Maths Solution:

e2x

sin 2x − 4e 3x

Find the following integrals in Exercises 6 to 20 :


Solution:


Solution:


Solution:


Solution:


Solution:

∫ ( + 1) dx4e3x

∫ (1 − ) dxx2 1x2

∫ + bx + c)dx(ax2

∫ ( + ) dx2x2 ex

∫ dx[ − ]x−−√ 1x√

2


Solution:


Solution:


Solution:


Solution:

∫ dx+ −4x3 5x2

x2

∫ dx+3x+4x3

x√

∫ dx− +x−1x3 x2

x−1

∫ (1 − x) dxx−−√


Solution:


Solution:


Solution:


Solution:


Solution:

∫ ( + 2x + 3) dxx−−√ 3x2

∫ (2x − 3cosx + )dxex

∫ ( − 3sinx + 5 ) dx2x2 x−−√

∫ secx(secx + tanx)dx

∫ dxxsec 2

xcosec 2


Solution:


The antiderivative equals

(a)

(b) (c) \frac { 2 }{ 3 } { x }^{ \frac { 3 }{ 2 } }+{ 2x }^{ \frac { 1 }{ 2 } }+c

(d) Solution:

Ex 7.1 Class 12 Maths Question 22.If such that f(2)=0 then f(x) is

(a) (b) { x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } +\frac { 129 }{ 8 }

(c)

(d) Solution:

∫ dx2−3sinxxcos2

( + )x−−√ 1x√

+ + c13x 1

3 2x 12

+ + c23x 2

3 x12

2

+ + c23x

32 2x 1

2

+ + c32x

32

12x 1

2

f(x) = −ddx 4x3 3

x4

+ −x4 1x3

1298

+ +x3 1x4

1298

+ +x4 1x3

1298

+ −x3 1x4

1298



Solution:


Solution:


Solution:

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

2x1+x2

(logx)2

x

1x+xlogx

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


Solution:


Solution:


Solution:

ax + b− −−−−√

x x + 2− −−−√

x 1 + 2x2− −−−−−√


Solution:


Solution:


Solution:


Solution:

(4x + 2) + x + 1x2− −−−−−−−√

1x− x√

, x > 0xx+4√

.− 1)(x313 x5


Solution:


Solution:


Solution:


x2

)(2+3x3 3

, x > 01x(logx)m

x9−4x2

Solution:


Solution:


Solution:


Solution:


e2x+3

xex2

e xtan −1

1+x2

−1e2x

+1e2x

Solution:

Ex 7.2 Class 12 Maths Question 21.tan²(2x-3)Solution:∫tan²(2x-3)dx = ∫[sec²(2x-3)-1]dx = Iput 2x-3 = tso that 2dx = dtI = ∫sec²t dt-x+c= = Ex 7.2 Class 12 Maths Question 22.sec²(7-4x)Solution:


Solution:


Solution:

−e2x e2x

+e2x e−2x

12t − x + c1

2tan(2x − 3) − x + c1

2

xsin −1

1−x2√

2cosx−3sinx6cosx+4sinx


Solution:


Solution:


Solution:


Solution:

1xcos2 (1−tanx) 2

cos x√x√

cos2xsin2x− −−−−√

cosx1+sinx√

Ex 7.2 Class 12 Maths Question 29.cotx log sinxSolution:


Solution:


Solution:


Solution:

sinx1+cosx

sinx(1+cosx) 2

11+cotx


Solution:


Solution:

11−tanx

tanx√sinxcosx


Solution:


Solution:


Solution:

(1+logx)2

x

(x+1)(x+logx) 2

x

dxsin( )x3 tan −1x4

1+x8


(a) 10x – x10 + C(b) 10x + x10 + C(c) (10x – x10) + C(d) log (10x + x10) + CSolution:


(a) tanx + cotx + c(b) tanx – cotx + c(c) tanx cotx + c(d) tanx – cot2x + cSolution:


Find the integrals of the functions in Exercises 1 to 22.Ex 7.3 Class 12 Maths Question 1.sin²(2x+5)Solution:

∫ dx+ log10x9 10x e10

+x10 10x

∫ =dxx xsin 2 cos2

Ex 7.3 Class 12 Maths Question 2.sin3x cos4xSolution:

Ex 7.3 Class 12 Maths Question 3.∫cos2x cos4x cos6x dxSolution:

Ex 7.3 Class 12 Maths Question 4.∫sin3(2x+1)dxSolution:

Ex 7.3 Class 12 Maths Question 5.sin3x cos3xSolution:

Ex 7.3 Class 12 Maths Question 6.sinx sin2x sin3xSolution:

Ex 7.3 Class 12 Maths Question 7.sin 4x sin 8xSolution:


Solution:


Solution:

Ex 7.3 Class 12 Maths Question 10.∫sinx4 dxSolution:

1−cosx1+cosx

cosx1+cosx

Ex 7.3 Class 12 Maths Question 11.cos4 2xSolution:


Solution:


Solution:

xsin 2

1+cosx

cos2x−cos2αcosx−cosα


Solution:


Solution:

cosx−sinx1+sin2x

∫ 2x sec2x dx = Itan 3

Ex 7.3 Class 12 Maths Question 16.tan4xSolution:


Solution:


Solution:


Solution:


Solution:

x+ xsin 3 cos3

x xsin 2 cos2

cos2x+ x2sin 2

xcos2

1sinx xcos3

cos2x(cosx+sinx) 2

Ex 7.3 Class 12 Maths Question 21.sin-1 (cos x)Solution:


Solution:


(a) tanx+cotx+c(b) tanx+cosecx+c(c) -tanx+cotx+c(d) tanx+secx+cSolution:


(a) -cot(e.xx)+c(b) tan(xex)+c(c) tan(ex)+c(d) cot ex+cSolution:

∫ dx1cos(x−a)cos(x−b)

∫ dx is equal tox− xsin 2 cos2

x xsin 2 cos2

∫ dx is equal to(1+x)ex

co ( .x)s2 ex

Integrals Class 12 Ex 7.4


Solution:


Solution:


Solution:


Solution:

3x2

+1x6

1

1+4x2√

1

+1(2−x)2√

1

9−25x2√


Solution:


Solution:


Solution:


Solution:

3x1+2x4

x2

1−x6

x−1

−1x2√

x2

+x6 a6√


Solution:


Solution:


Solution:


Solution:

xsec 2

x+4tan 2√

1+2x+2x2√

1+6x+59x2

17−6x−x2√


Solution:


Solution:

1(x−1)(x−2)√

18+3x−x2√


Solution:


Solution:

1(x−a)(x−b)√

4x+1

+x−32x2√


Solution:


Solution:put 5x-2=A (1+2x+3x²)+B

⇒ 6A=5, A= , B=

x+2

−1x2√

5x−21+2x+3x2

ddx

− 2 = 2A + B56 − 11

3


Solution:

6x+7(x−5)(x−4)√


Solution:

x+2

4x−x2√


Solution:


Solution:

x+2

+2x+3x2√

x+3−2x−5x2


Solution:

5x+3

+4x+10x2√


(a) xtan-1(x+1)+c(b) (x+1)tan-1x+c(c) tan-1(x+1)+c(d) tan-1x+cSolution:


(a)

(b)

(c)

∫ equalsdx+2x+2x2

∫ equalsdx9x−4x2√

( ) + c19sin −1 9x−8

8

( ) + c12sin −1 8x−9

9

( ) + c13sin −1 9x−8

8

(d)

Solution:



Solution:


Solution:

( ) + csin −1 9x−89

x(x+1)(x+2)

1−9x2


Solution:


Solution:


Solution:

3x−1(x−1)(x−2)(x−3)

x(x−1)(x−2)(x−3)

2x+3x+2x2


Solution:


Solution:

1−x2

x(1−2x)

x( +1)(x−1)x2


Solution:


Solution:

x(x+2)(x−1)2

3x+5− −x+1x3 x2


Solution:


Solution:

2x−3( −1)(2x+3)x2

5x(x−1)( −4)x2


Solution:


Solution:

+x+1x3

−1x2

2(1−x)(1+ )x2


Solution:


Solution:

3x−1

(x+2)2

1−1x4


[Hint : multiply numerator and denominator by xn-1 and put xn = t ]Solution:


Solution:

1x( +1)xn

cosx(1−sinx)(2−sinx)


Solution:

( +1)( +2)x2 x2

( +3)( +4)x2 x2


Solution:


Solution:

2x( +1)( +3)x2 x2

1x( −1)x4


Solution:

Ex 7.5 Class 12 Maths Question 22.choose the correct answer in each of the following :

(a)

(b)

1−1ex

∫ equalsxdx(x−1)(x−2)

log + c∣∣∣

(x−1)2

x−2∣∣∣

log + c∣∣∣

(x−2)2

x−1∣∣∣

(c)

(d) log|(x-1)(x-2)|+cSolution:


(a) (b) (c) (d) Solution:


Ex 7.6 Class 12 Maths Question 1.x sinxSolution:


log ( ) + c∣∣

x−12

x−2∣∣

∫ equalsdxx( +1)x2

log|x| − log( + 1) + c12 x2

log|x| + log( + 1) + c12 x2

−log|x| + log( + 1) + c12 x2

log|x| + log( + 1) + c12 x2

x sin3xSolution:


Solution:

Ex 7.6 Class 12 Maths Question 4.x logxSolution:

Ex 7.6 Class 12 Maths Question 5.x log2xSolution:


x2ex

Solution:


Solution:


Solution:


Solution:

logxx2

x xsin −1

x xtan −1

x xcos−1


Solution:x(sin −1 )2


Solution:

Ex 7.6 Class 12 Maths Question 12.x sec²xSolution:


Solution:

Ex 7.6 Class 12 Maths Question 14.x(logx)²Solution:

Ex 7.6 Class 12 Maths Question 15.(x²+1)logxSolution:

x xcos−1

1−x2√

ta xn−1


Solution:


Solution:

(sinx + cosx)ex

xex

(1+x)2


Solution:


Solution:

(1+sinx)ex

1+cosx

( − )ex 1x

1x2


Solution:


Solution:


Solution:

(x−2)e x

(x−1)3

sinxe2x

( )sin −1 2x1+x2


(a)

(b)

(c)

(d) Solution:



Class 12 Integrals Ex 7.7


Solution:

∫ dx equalsx2ex3

+ c13ex3

+ + c13 ex2

+ c12ex3

+ c12ex2

∫ secx(1 + tanx)dx equalsex

cosx + cex

secx + cex

sinx + cex

tanx + cex

4 − x2− −−−−√


Solution:


Solution:


Solution:


Solution:

1 − 4x2− −−−−−√

+ 4x + 6x2− −−−−−−−−√

+ 4x + 1x2− −−−−−−−−√

1 − 4x − x2− −−−−−−−−√


Solution:


Solution:


Solution:

+ 4x − 5x2− −−−−−−−−√

1 + 3x − x2− −−−−−−−−√

+ 3xx2− −−−−−√


Solution:


(a)

(b)

(c)

(d) Solution:


Solution:

1 + x2

9

− −−−−√

∫ dx is equal to1 + x2− −−−−√+ log|x + | + cx

2 1 + x2− −−−−√ 12 1 + x2− −−−−√

+ c23(1 + )x2

32

x + c23 (1 + )x2

32

+ log x + + cx2

2 1 + x2− −−−−√ 12x2 ∣∣ 1 + x2− −−−−√ ∣∣

∫ dx is equal to− 8x + 7x2− −−−−−−−−√



Solution:


Solution:

x dx∫ ba

(x + 1)dx∫ 50


Solution:dx∫ 3

2 x2


Solution:( − x)dx∫ 4

1 x2


Solution:dx∫ 1

−1 ex


Solution:



)dx∫ 40 (x + e2x

(x + 1)dx

Solution:


Solution:


Solution:


Solution:

(x + 1)dx∫ 1−1

dx∫ 32

1x

( − + 6x + 9) dx∫ 21 4x3 5x2

sin2x dx∫π4

0


Solution:


Solution:


Solution:

cos2x dx∫π2

0

dx∫ 54 ex

tanx dx∫π4

0


Solution:


Solution:


Solution:

cosec xdx∫π4

π6

∫ 10

dx1−x2√

∫ 10

dx1+x2


Solution:


Solution:


Solution:


Solution:

∫ 32

dx−1x2

xdx∫π2

0 cos2

dx∫ 32

x+1x2

dx∫ 10

2x+3+15x2


Solution:


Solution:

dx∫ 10 xex2

dx∫ 21

5x2

+4x+3x2


Solution:( x + + 2) dx∫

π4

0 2sec2 x3


Solution:


Solution:


Solution:

( − )dx∫ π0 sin 2 x

2 cos2 x2

dx∫ 20

6x+3+4x2

( + sin ) dx∫ 10 xex πx

4


(a)

(b) (c) (d) Solution:



equals∫ 3√1

dx1+x2

π32π3π

6π12

equals∫23

0dx

4+9x2π6π12π24π4

Integration Class 12 Ex 7.10

Ex 7.10 Class 12 Maths Question 1:

Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:

NCERT Solutions for Class 2 Maths Integration Class 12 Ex 7.11

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise

Miscellaneous Exercise Class 11 Maths Question 1:

Solution:


Solution:


Solution:

vMiscellaneous Exercise Class 11 Maths Question 4:

Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:


Solution:

Question 35:

Solution:


Solution:


Solution:


Solution:


Solution:



Solution:

Integration Formulas

integrals ex 7.1 class 12 - fliplearn

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