NCERT Solutions Exercise- 7.2: Integrals

# NCERT Solutions Class 12 Maths Chapter 7 - Integrals

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N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 2
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e 	 1 	 t o 	 8 .
1 .
A n s . 	 P u t t i n g

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2 .
A n s . 	 P u t t i n g

Page 2

N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 2
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e 	 1 	 t o 	 8 .
1 .
A n s . 	 P u t t i n g

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2 .
A n s . 	 P u t t i n g

2 	/ 	 2 9

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3 .
A n s . 	 P u t t i n g

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Page 3

N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 2
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e 	 1 	 t o 	 8 .
1 .
A n s . 	 P u t t i n g

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2 .
A n s . 	 P u t t i n g

2 	/ 	 2 9

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3 .
A n s . 	 P u t t i n g

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3 	/ 	 2 9
4 .
A n s . 	 P u t t i n g

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5 .
A n s .
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= 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 [ 	 	 b e c a u s e ]
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Page 4

N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 2
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e 	 1 	 t o 	 8 .
1 .
A n s . 	 P u t t i n g

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=

2 .
A n s . 	 P u t t i n g

2 	/ 	 2 9

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=
=
3 .
A n s . 	 P u t t i n g

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=
=
3 	/ 	 2 9
4 .
A n s . 	 P u t t i n g

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5 .
A n s .
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6 .
A n s .
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U s i n g 	 	 	 	 W e 	 h a v e
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7 .
A n s .
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U s i n g

Page 5

N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 2
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e 	 1 	 t o 	 8 .
1 .
A n s . 	 P u t t i n g

=
=

2 .
A n s . 	 P u t t i n g

2 	/ 	 2 9

=
=
=
3 .
A n s . 	 P u t t i n g

=
=
=
3 	/ 	 2 9
4 .
A n s . 	 P u t t i n g

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5 .
A n s .
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= 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 [ 	 	 b e c a u s e ]
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6 .
A n s .
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U s i n g 	 	 	 	 W e 	 h a v e
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7 .
A n s .
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U s i n g

5 	 / 	 2 9
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8 .
A n s . 	 L e t 	 I 	 =
= 	 	 … … … . ( i )
P u t t i n g

F r o m 	 e q . 	 ( i ) ,
I 	 =
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=
=
```

## Mathematics (Maths) for JEE Main & Advanced

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## FAQs on NCERT Solutions Class 12 Maths Chapter 7 - Integrals

 1. What are integrals and how are they used in mathematics?
Ans. Integrals are mathematical tools used to calculate the area under curves or to find the accumulation of quantities over a given interval. They are widely used in various fields of mathematics and physics, such as finding the area of irregular shapes, calculating the displacement of an object, or determining the probability distribution of a random variable.
 2. What is the difference between indefinite and definite integrals?
Ans. An indefinite integral represents a family of functions that differ only by a constant, whereas a definite integral gives a specific numerical value. In other words, an indefinite integral does not have upper and lower limits, while a definite integral is evaluated over a specific interval.
 3. How can we find the integral of a function?
Ans. To find the integral of a function, we can use various techniques such as the power rule, substitution method, integration by parts, or trigonometric substitutions. The choice of method depends on the complexity of the function and the available tools.
 4. What are the applications of integrals in real life?
Ans. Integrals have numerous applications in real-life situations. They are used in physics to calculate the work done in moving an object, in economics to determine the total revenue or cost functions, in engineering to find the center of mass of an object, and in biology to model population growth, among many other applications.
 5. Is there any relationship between derivatives and integrals?
Ans. Yes, derivatives and integrals are closely related. The derivative of a function represents its rate of change, while the integral represents the accumulation of the function over a given interval. The Fundamental Theorem of Calculus states that differentiation and integration are inverse processes, meaning that taking the derivative of an integral gives back the original function.

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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