NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11.

- Integrals Class 12 Ex 7.1
- Integrals Class 12 Ex 7.2
- 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

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 12 |

Subject |
Maths |

Chapter |
Chapter 7 |

Chapter Name |
Integrals |

Exercise |
Ex 7.11 |

Number of Questions Solved |
21 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.11

**By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19.**

**Ex 7.11 Class 12 Maths Question 1.**

**Solution:**

**Ex 7.11 Class 12 Maths Question 2.**

**Solution:**

let I =

**Ex 7.11 Class 12 Maths Question 3.**

**Solution:**

let I =

**Ex 7.11 Class 12 Maths Question 4.**

**Solution:**

let I =

**Ex 7.11 Class 12 Maths Question 5.**

**Solution:**

at x = – 5, x + 2 < 0; at x = – 2, x + 2 = 0; at x = 5, x + 2>0;x + 2<0, x + 2 = 0, x + 2>0

**Ex 7.11 Class 12 Maths Question 6.**

**Solution:**

**Ex 7.11 Class 12 Maths Question 7.**

**Solution:**

**Ex 7.11 Class 12 Maths Question 8.**

**Solution:**

let I =

**Ex 7.11 Class 12 Maths Question 9.**

**Solution:**

let 2-x = t

⇒ – dx = dt

when x = 0, t = 2 and when x = 2,t = 0

**Ex 7.11 Class 12 Maths Question 10.**

**Solution:**

**Ex 7.11 Class 12 Maths Question 11.**

**Solution:**

Let f(x) = sin² x

f(-x) = sin² x = f(x)

∴ f(x) is an even function

**Ex 7.11 Class 12 Maths Question 12.**

**Solution:**

let I = …(i)

**Ex 7.11 Class 12 Maths Question 13.**

**Solution:**

Let f(x) = sin^{7} xdx

⇒ f(-x) = -sin^{7} x = -f(x)

⇒ f(x) is an odd function of x

⇒

**Ex 7.11 Class 12 Maths Question 14.**

**Solution:**

let f(x) = cos^{5} x

⇒ f(2π – x) = cos^{5} x

**Ex 7.11 Class 12 Maths Question 15.**

**Solution:**

let I = …(i)

**Ex 7.11 Class 12 Maths Question 16.**

**Solution:**

let I =

then I =

**Ex 7.11 Class 12 Maths Question 17.**

**Solution:**

let I = …(i)

**Ex 7.11 Class 12 Maths Question 18.**

**Solution:**

**Ex 7.11 Class 12 Maths Question 19.**

show that if f and g are defined as f(x)=f(a-x) and g(x)+g(a-x)=4

**Solution:**

let I =

**Ex 7.11 Class 12 Maths Question 20.**

The value of is

(a) 0

(b) 2

(c) π

(d) 1

**Solution:**

(c) let I = is

**Ex 7.11 Class 12 Maths Question 21.**

The value of is

(a) 2

(b)

(c) 0

(d) -2

**Solution:**

let I =

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