## NCERT Solutions for Class 12 Maths Exercise 7.10 hapter 7 Integrals – FREE PDF Download

NCERT Solutions for integrals Class 12 exercises 7.10 are accessible in PDF format which is available at CoolGyan’s online learning portal. The solutions to this particular exercise from chapter 7 Integrals have been prepared by our experts who have years of experience in this field. Students can find, well-explained solutions to maths problems at CoolGyan’s online learning portal. All the solutions are provided in a way that will help you in understanding the concept effectively. You can download them in PDF format for free.

# NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.10) Exercise 7.10

**Evaluate the integrals in Exercises 1 to 8 using substitutions.**

**1. **

**Ans. **Let I =

= ……….(i)

Putting

To change the limits of integration from x to t

when x = 0, t = x^{2} +1 = 0 +1 = 1

when x =1, t = x^{2} +1 = 1 +1 = 2

From eq. (i),

=

=

=

=

= Ans.

**2. **

**Ans. **Let I = ……….(i)

Putting

To change the limits of integration from to

When

When

From eq. (i),

I =

=

=

=

=

=

=

=

=23(t32)10+211(t112)10−47(t72)10=23(t32)01+211(t112)01−47(t72)01

=

=

=

= Ans.

**3. **

**Ans. **Let I = ……….(i)

Putting

Limits of integration, when

when

From eq. (i),

I =

=

=

=

[Applying Product Rule]

=

=

=

=

=

=

=

= Ans.

**4. **

**Ans. **Let I = ……….(i)

Putting

Limits of integration when and when

From eq. (i),

I =

=

=

=

=

=

=

=

=

= Ans.

**5. **

**Ans. **Let I =

= ……….(i)

Putting

Limits of integration when and when

From eq. (i), I =

=

=

=

= Ans.

**6. **

**Ans. **

=

=

=

=

=

=

=

=

=117√log(17√+317√−3×17√+117√−1)=117log(17+317−3×17+117−1)

=

=

=

=

=

=

= Ans.

**7. **

**Ans. **Let I =

=

= ……….(i)

Putting

Limits of integration when and when

From eq. (i), I =

=

=

=

= Ans.

**8. **

**Ans. **Let I = ……….(i)

Putting

Limits of integration when and when

From eq. (i),

I =

=

=

=

=

=

=(ett)42=(ett)24

=

=

= Ans.

**Choose the correct answer in Exercises 9 and 10.**

**9. The value of the integral is:**

**(A) 6**

**(B) 0**

**(C) 3**

**(D) 4**

**Ans. **Let I =

=

=

=

= ……….(i)

Putting

Limits of integration when

and when

From eq. (i),

I =

=

=

=

=

=

Therefore, option (A) is correct.

**10. If then is:**

**(A) **

**(B) **

**(C) **

**(D) **

**Ans.**

=

[Applying Product Rule]

=

=

=

=

=

Therefore, option (B) is correct.