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Rajesh Madan'S: Mathematics Classes

This document contains 13 questions related to indefinite integration, definite integration, and differential equations across 4 sets. The questions cover topics like evaluating integrals, solving differential equations, and finding areas bounded by curves using integration. Each set contains multiple choice questions worth 4 marks each, with a maximum time of 90 minutes and total marks of 52 per set.

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Pratham Malhotra
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340 views8 pages

Rajesh Madan'S: Mathematics Classes

This document contains 13 questions related to indefinite integration, definite integration, and differential equations across 4 sets. The questions cover topics like evaluating integrals, solving differential equations, and finding areas bounded by curves using integration. Each set contains multiple choice questions worth 4 marks each, with a maximum time of 90 minutes and total marks of 52 per set.

Uploaded by

Pratham Malhotra
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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RAJESH MADAN’S

MATHEMATICS CLASSES
( R . M. M . C )
ASHOK NAGAR, SUBHASH NAGAR & VIKAS PURI
Ph. 9810655836

TEST OF INDEFINITE INTEGRATION,


DEFINITE INTEGRATION, APPLICATIONS
OF INTEGRATION AND DIFFERENTIAL
EQUATIONS

Max. Time : 90 Min SET – 1 Max. Marks : 52

Each Question carries 4 marks

e2x  1
Q.1 Evaluate :  e2x  1 dx

 7x  1
Q.2 Evaluate :  1  5x  6x2 dx

1 x
Q.3 Evaluate :  tan1 dx
1 x

Q.4 Solve the differential equation : (ex + 1) y . dy = (y + 1) . ex . dx

Q.5 Solve the differential equation : (x3 + 3xy2)dx + (y3 + 3x2 y)dy=0

dy
Q.6 Solve the differential equation :  2y tan x  sin x ; given that y = 0
dx

and x  .
3
dy
Q.7 Solve the differential equation : e dx   x  1 given that x = 0, y = 3.

 /3
dx
Q.8 Evaluate :  1  tan x
 /6

2
log x
Q.9 Evaluate :  dx
1 x2


x sin x dx
Q.10 Solve using properties :  1  cos2 x
0


 1  x  sin x cos2 x dx
2
Q.11 Solve using properties :


2
Q.12 Evaluate :  x 3  x dx
1

Q.13 Find the area bounded by the circle x 2  y 2  16 and the line
3 y  x , in the first quadrant, enclosed by x – axis using integration.
RAJESH MADAN’S
MATHEMATICS CLASSES
( R . M. M . C )
ASHOK NAGAR, SUBHASH NAGAR & VIKAS PURI
Ph. 9810655836

TEST OF INDEFINITE INTEGRATION,


DEFINITE INTEGRATION, APPLICATIONS
OF INTEGRATION AND DIFFERENTIAL
EQUATIONS

Max. Time : 90 Min SET – 2 Max. Marks : 52

Each Question carries 4 marks

e x  x  1
Q.1 Evaluate :  cos2 dx
 
x ex

Q.2 Evaluate :
 x  2  dx

5  12x  9x 2

dx
Q.3 Evaluate :  3/4

x2 x 4  1 
 dy   dy 
Q.4 Solve the differential equation : y  x    a  y 2 
 dx   dx 

Q.5 Solve the differential equation :


y  y 
x  sin    dy   y  sin    x  dx  0
x  x 

 dy  x
Q.6 Solve the differential equation :    y  tan x  e  sec x
 dx 
x 2 y
Q.7 Solve the differential equation : e 1  y dx  dy  0 , given that
x
y = 1, when x = 0

 /3
dx
Q.8 Evaluate :  1  cot x
 /6

 /2
Q.9 Evaluate :  cos   sin3  d
0


x tan x dx
Q.10 Solve by using properties :  sec x  tan x
0

4
Q.11 Solve by using properties :   x  1  x  2  x  3  dx
1


2
Q.12 Evaluate :   cosax  sinax  dx


Q.13 Using integration, find the area of region bounded by the triangle
whose vertices are (–2, 1), (0, 4) and (2, 3).
RAJESH MADAN’S
MATHEMATICS CLASSES
( R . M. M . C )
ASHOK NAGAR, SUBHASH NAGAR & VIKAS PURI
Ph. 9810655836

TEST OF INDEFINITE INTEGRATION,


DEFINITE INTEGRATION, APPLICATIONS
OF INTEGRATION AND DIFFERENTIAL
EQUATIONS

Max. Time : 90 Min SET – 3 Max. Marks : 52

Each Question carries 4 marks

 sin3 x  cos3 x  dx
Q.1 Evaluate :  sin2 x cos2 x

x dx
Q.2 Evaluate :  x3  x 2  x  1

 x2  1  ex dx
Q.3 Evaluate : 
 x  12

Q.4 Solve the differential equation : x.cos y.dy = (x . ex . log x + ex).dx

Q.5 Solve the differential equation : x dy  y dx  x 2  y 2 dx , given that


y = 0, when x = 1.

 dy 
Q.6 Solve the differential equation :    y  tan x  xm  cos x
 dx 

 dy 
Q.7 Solve the differential equation : log    ax  by
 dx 
a
ax
Q.8 Evaluate :  dx
ax
a

 /2
sin2 d
Q.9 Evaluate :  sin4   cos 4 
0


x tan x dx
Q.10 Solve by using properties :  sec x cosec x
0

3/2
Q.11 Solve by using properties :  x sin x dx
1

 /4
sin x  cos x
Q.12 Evaluate :  dx
9  16 sin 2x
0

Q.13 Using integration, find the area of the region in the first quadrant,
enclosed by the x – axis, the line y = x and the circle x2 + y2 = 32
RAJESH MADAN’S
MATHEMATICS CLASSES
( R . M. M . C )
ASHOK NAGAR, SUBHASH NAGAR & VIKAS PURI
Ph. 9810655836

TEST OF INDEFINITE INTEGRATION,


DEFINITE INTEGRATION, APPLICATIONS
OF INTEGRATION AND DIFFERENTIAL
EQUATIONS

Max. Time : 90 Min SET – 4 Max. Marks : 52

Each Question carries 4 marks

Q.1 Evaluate :  sec 2 x cosec 2 x dx

 3 sin x  2 cos x
Q.2 Evaluate :  13  cos2 x  7 sin x dx

Q.3 Evaluate :  tan3 2x sec 2x dx

Q.4 Solve the differential equation : 


x 2

dy e sin x  sin2x 
dx y  2 log y  1

 dy 
Q.5 Solve the differential equation : x    y  log y  log x  1
 dx 

dy
Q.6 Solve the differential equation :  x  y  xy  1
dx

 e2 x y  dx
Q.7 Solve the differential equation :    1
 x x  dy
 
2
x dx
Q.8 Solve by using properties :  3x  x
1

1
2x  3
Q.9 Evaluate :  5x2  1 dx
0

 /4
Q.10 Solve by using properties :  log 1  tan x  dx
0

5
Q.11 Solve by using properties :   x  2  x  3  x  5  dx
2

 /2
Q.12 Evaluate :  sin2x tan1  sin x  dx
0

Q.13 Using integration, find the area of the triangle whose vertices are
(2, 3), (3, 5) and (4, 4).

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