NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2.

- Integrals Class 12 Ex 7.1
- Integrals Class 12 Ex 7.3
- Integrals Class 12 Ex 7.4
- Integrals Class 12 Ex 7.5
- Integrals Class 12 Ex 7.6
- Integrals Class 12 Ex 7.7
- Integrals Class 12 Ex 7.8
- Integrals Class 12 Ex 7.9
- Integrals Class 12 Ex 7.10
- Integrals Class 12 Ex 7.11

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 12 |

Subject |
Maths |

Chapter |
Chapter 7 |

Chapter Name |
Integrals |

Exercise |
Ex 7.2 |

Number of Questions Solved |
39 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2

**Integrate the functions in Exercises 1 to 37:**

**Ex 7.1 Class 12 Maths Question 1.**

**Solution:**

Let 1+x² = t

⇒ 2xdx = dt

**Ex 7.2 Class 12 Maths Question 2.**

**Solution:**

Let logx = t

⇒

**Ex 7.2 Class 12 Maths Question 3.**

**Solution:**

Put 1+logx = t

∴

= log|1+logx|+c

**Ex 7.2 Class 12 Maths Question 4.**

sinx sin(cosx)

**Solution:**

Put cosx = t, -sinx dx = dt

**Ex 7.2 Class 12 Maths Question 5.**

sin(ax+b) cos(ax+b)

**Solution:**

let sin(ax+b) = t

⇒ cos(ax+b)dx = dt

**Ex 7.2 Class 12 Maths Question 6.**

**Solution:**

**Ex 7.2 Class 12 Maths Question 7.**

**Solution:**

Let x+2 = t²

⇒ dx = 2t dt

**Ex 7.2 Class 12 Maths Question 8.**

**Solution:**

let 1+2x² = t²

⇒ 4x dx = 2t dt

**Ex 7.2 Class 12 Maths Question 9.**

**Solution:**

let x²+x+1 = t

⇒(2x+1)dx = dt

**Ex 7.2 Class 12 Maths Question 10.**

**Solution:**

Let √x-1 = t

= 2logt + c

= 2log(√x-1)+c

**Ex 7.2 Class 12 Maths Question 11.**

**Solution:**

let x+4 = t

⇒ dx = dt, x = t-4

**Ex 7.2 Class 12 Maths Question 12.**

**Solution:**

**Ex 7.2 Class 12 Maths Question 13.**

**Solution:**

Let 2+3x³ = t

⇒ 9x² dx = dt

**Ex 7.2 Class 12 Maths Question 14.**

**Solution:**

Put log x = t, so that

**Ex 7.2 Class 12 Maths Question 15.**

**Solution:**

put 9-4x² = t, so that -8x dx = dt

**Ex 7.2 Class 12 Maths Question 16.**

**Solution:**

put 2x+3 = t

so that 2dx = dt

**Ex 7.2 Class 12 Maths Question 17.**

**Solution:**

Let x² = t

⇒ 2xdx = dt ⇒

**Ex 7.2 Class 12 Maths Question 18.**

**Solution:**

**Ex 7.2 Class 12 Maths Question 19.**

**Solution:**

put e^{x}+e^{-x} = t

so that (e^{x}-e^{-x})dx = dt

**Ex 7.2 Class 12 Maths Question 20.**

**Solution:**

put e^{2x}-e^{-2x} = t

so that (2e^{2x}-2e^{-2x})dx = dt

**Ex 7.2 Class 12 Maths Question 21.**

tan²(2x-3)

**Solution:**

∫tan²(2x-3)dx = ∫[sec²(2x-3)-1]dx = I

put 2x-3 = t

so that 2dx = dt

I = ∫sec²t dt-x+c

=

=

**Ex 7.2 Class 12 Maths Question 22.**

sec²(7-4x)

**Solution:**

∫sec²(7-4x)dx

=

**Ex 7.2 Class 12 Maths Question 23.**

**Solution:**

**Ex 7.2 Class 12 Maths Question 24.**

**Solution:**

put 2sinx+4cosx = t

⇒ (2cosx-3sinx)dx = dt

**Ex 7.2 Class 12 Maths Question 25.**

**Solution:**

put 1-tanx = t

so that -sec²x dx = dt

**Ex 7.2 Class 12 Maths Question 26.**

**Solution:**

= 2sin√x+c

**Ex 7.2 Class 12 Maths Question 27.**

**Solution:**

put sin2x = t²

⇒ cos2x dx = t dt

**Ex 7.2 Class 12 Maths Question 28.**

**Solution:**

put 1+sinx = t²

⇒cosx dx = 2t dt

**Ex 7.2 Class 12 Maths Question 29.**

cotx log sinx

**Solution:**

put log sinx = t,

⇒ cot x dx = dt

**Ex 7.2 Class 12 Maths Question 30.**

**Solution:**

put 1+cosx = t

⇒ -sinx dx = dt

=-log(1+cosx)+c

**Ex 7.2 Class 12 Maths Question 31.**

**Solution:**

put 1+cosx = t

so that -sinx dx = dt

**Ex 7.2 Class 12 Maths Question 32.**

**Solution:**

**Ex 7.2 Class 12 Maths Question 33.**

**Solution:**

**Ex 7.2 Class 12 Maths Question 34.**

**Solution:**

**Ex 7.2 Class 12 Maths Question 35.**

**Solution:**

let 1+logx = t

⇒

**Ex 7.2 Class 12 Maths Question 36.**

**Solution:**

put x+logx = t

**Ex 7.2 Class 12 Maths Question 37.**

**Solution:**

**Choose the correct answer in exercises 38 and 39**

**Ex 7.2 Class 12 Maths Question 38.**

(a) 10^{x} – x^{10} + C

(b) 10^{x} + x^{10} + C

(c) (10^{x} – x^{10}) + C

(d) log (10^{x} + x^{10}) + C

**Solution:**

(d)

= log (10^{x} + x^{10}) + C

**Ex 7.2 Class 12 Maths Question 39.**

(a) tanx + cotx + c

(b) tanx – cotx + c

(c) tanx cotx + c

(d) tanx – cot2x + c

**Solution:**

(c)

= tanx – cotx + c

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