# Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 6 - Definite Integration [Latest edition]

## Chapter 6: Definite Integration

Exercise 6.1Exercise 6.2Miscellaneous Exercise 6
Exercise 6.1 [Page 145]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 6 Definite Integration Exercise 6.1 [Page 145]

Exercise 6.1 | Q 1 | Page 145

Evaluate the following definite integrals: int_4^9 (1)/sqrt(x)*dx

Exercise 6.1 | Q 2 | Page 145

Evaluate the following definite integrals: int_(-2)^3 (1)/(x + 5)*dx

Exercise 6.1 | Q 3 | Page 145

Evaluate the following definite integrals: int_2^3 x/(x^2 - 1)*dx

Exercise 6.1 | Q 4 | Page 145

Evaluate the following definite integrals: int_0^1 (x^2 + 3x + 2)/sqrt(x)*dx

Exercise 6.1 | Q 5 | Page 145

Evaluate the following definite integrals: int_2^3 x/((x + 2)(x + 3))*dx

Exercise 6.1 | Q 6 | Page 145

Evaluate the following definite integrals: int_1^2 dx/(x^2 + 6x + 5)

Exercise 6.1 | Q 7 | Page 145

Evaluate the following definite integrals: If int_0^"a" (2x + 1)*dx = 2, find the real value of a.

Exercise 6.1 | Q 8 | Page 145

Evaluate the following definite integrals: if int_1^"a" (3x^2 + 2x + 1)*dx = 11, find a.

Exercise 6.1 | Q 9 | Page 145

Evaluate the following definite integrals: int_0^1 (1)/(sqrt(1 + x) + sqrt(x))*dx

Exercise 6.1 | Q 10 | Page 145

Evaluate the following definite integrals: int_1^2 (3x)/((9x^2 - 1))*dx

Exercise 6.1 | Q 11 | Page 145

Evaluate the following definite integrals: int_1^3 logx*dx

Exercise 6.2 [Page 148]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 6 Definite Integration Exercise 6.2 [Page 148]

Exercise 6.2 | Q 1 | Page 148

Evaluate the following integrals : int_(-9)^9 x^3/(4 - x^2)*dx

Exercise 6.2 | Q 2 | Page 148

Evaluate the following integrals : int_0^"a" x^2("a" - x)^(3/2)*dx

Exercise 6.2 | Q 3 | Page 148

Evaluate the following integrals : int_1^3 (root(3)(x + 5))/(root(3)(x + 5) + root(3)(9 - x))*dx

Exercise 6.2 | Q 4 | Page 148

Evaluate the following integrals : int_2^5 sqrt(x)/(sqrt(x) + sqrt(7 - x))*dx

Exercise 6.2 | Q 5 | Page 148

Evaluate the following integrals : int_1^2 sqrt(x)/(sqrt(3 - x) + sqrt(x))*dx

Exercise 6.2 | Q 6 | Page 148

Evaluate the following integrals : int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx

Exercise 6.2 | Q 7 | Page 148

Evaluate the following integrals : int_0^1 log(1/x - 1)*dx

Exercise 6.2 | Q 8 | Page 148

Evaluate the following integrals : int_0^1 x(1 - x)^5 *dx

Miscellaneous Exercise 6 [Pages 148 - 150]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 6 Definite Integration Miscellaneous Exercise 6 [Pages 148 - 150]

Miscellaneous Exercise 6 | Q 1.01 | Page 148

Choose the correct alternative :

int_(-9)^9 x^3/(4 - x^2)*dx =

• 0

• 3

• 9

• – 9

Miscellaneous Exercise 6 | Q 1.02 | Page 148

Choose the correct alternative :

int_(-2)^3 dx/(x + 5) =

• -log(8/3)

• log(8/3)

• log(3/8)

• -log(3/8)

Miscellaneous Exercise 6 | Q 1.03 | Page 148

Choose the correct alternative :

int_2^3 x/(x^2 - 1)*dx =

• log (8/3)

• -log (8/3)

• (1)/(2)log(8/3)

• (-1)/(2)log(8/3)

Miscellaneous Exercise 6 | Q 1.04 | Page 149

Choose the correct alternative :

int_4^9 dx/sqrt(x) =

• 9

• 4

• 2

• 0

Miscellaneous Exercise 6 | Q 1.05 | Page 149

Choose the correct alternative :

If int_0^"a" 3x^2*dx = 8, then a = ?

• 2

• 0

• (8)/(3)

• a

Miscellaneous Exercise 6 | Q 1.06 | Page 149

Choose the correct alternative :

int_2^3 x^4*dx =

• (1)/(2)

• (5)/(2)

• (5)/(211)

• (211)/(5)

Miscellaneous Exercise 6 | Q 1.07 | Page 149

Choose the correct alternative :

int_0^2 e^x*dx =

• e – 1

• 1 – e

• 1 – e2

• e2 – 1

Miscellaneous Exercise 6 | Q 1.08 | Page 149

Choose the correct alternative :

int_"a"^"b" f(x)*dx =

• int_"b"^"a" f(x)*dx

• -int_"a"^"b" f(x)*dx

• -int_"b"^"a" f(x)*dx

• int_"0"^"a" f(x)*dx

Miscellaneous Exercise 6 | Q 1.09 | Page 149

Choose the correct alternative :

int_(-7)^7 x^3/(x^2 + 7)*dx =

• 7

• 49

• 0

• (7)/(2)

Miscellaneous Exercise 6 | Q 1.1 | Page 149

Choose the correct alternative :

int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx =

• (7)/(2)

• (5)/(2)

• 7

• 2

Miscellaneous Exercise 6 | Q 2.01 | Page 149

Fill in the blank : int_0^2 e^x*dx = ________

Miscellaneous Exercise 6 | Q 2.02 | Page 149

Fill in the blank : int_2^3 x^4*dx = _______

Miscellaneous Exercise 6 | Q 2.03 | Page 149

Fill in the blank : int_0^1 dx/(2x + 5) = _______

Miscellaneous Exercise 6 | Q 2.04 | Page 149

Fill in the blank : If int_0^"a" 3x^2*dx = 8, then a = _______

Miscellaneous Exercise 6 | Q 2.05 | Page 149

Fill in the blank : int_4^9 (1)/sqrt(x)*dx = _______

Miscellaneous Exercise 6 | Q 2.06 | Page 149

Fill in the blank : int_2^3 x/(x^2 - 1)*dx = _______

Miscellaneous Exercise 6 | Q 2.07 | Page 149

Fill in the blank : int_(-2)^3 dx/(x + 5) = _______

Miscellaneous Exercise 6 | Q 2.08 | Page 149

Fill in the blank : int_(-9)^9 x^3/(4 - x^2)*dx = _______

Miscellaneous Exercise 6 | Q 3.01 | Page 149

State whether the following is True or False : int_"a"^"b" f(x)*dx = int_(-"b")^(-"a") f(x)*dx

• True

• False

Miscellaneous Exercise 6 | Q 3.02 | Page 149

State whether the following is True or False : int_"a"^"b" f(x)*dx = int_"a"^"b" f("t")*dt

• True

• False

Miscellaneous Exercise 6 | Q 3.03 | Page 149

State whether the following is True or False : int_0^"a" f(x)*dx = int_"a"^0 f("a" - x)*dx

• True

• False

Miscellaneous Exercise 6 | Q 3.04 | Page 149

State whether the following is True or False : int_"a"^"b" f(x)*dx = int_"a"^"b" f(x - "a" - "b")*dx

• True

• False

Miscellaneous Exercise 6 | Q 3.05 | Page 149

State whether the following is True or False : int_(-5)^(5)  x^3/(x^2 + 7)*dx = 0

• True

• False

Miscellaneous Exercise 6 | Q 3.06 | Page 150

State whether the following is True or False :  int_1^2 sqrt(x)/(sqrt(3 - x) + sqrt(x))*dx = (1)/(2)

• True

• False

Miscellaneous Exercise 6 | Q 3.07 | Page 150

State whether the following is True or False :  int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx = (9)/(2)

• True

• False

Miscellaneous Exercise 6 | Q 3.08 | Page 150

State whether the following is True or False : int_4^7 ((11 - x)^2)/((11 - x)^2 + x^2)*dx = (3)/(2)

• True

• False

Miscellaneous Exercise 6 | Q 4.01 | Page 150

Solve the following : int_2^3 x/((x + 2)(x + 3))*dx

Miscellaneous Exercise 6 | Q 4.02 | Page 150

Solve the following : int_1^2 (x + 3)/(x (x + 2))*dx

Miscellaneous Exercise 6 | Q 4.03 | Page 150

Solve the following : int_1^3 x^2 log x*dx

Miscellaneous Exercise 6 | Q 4.04 | Page 150

Solve the following : int_0^1 e^(x^2)*x^3dx

Miscellaneous Exercise 6 | Q 4.05 | Page 150

Solve the following : int_1^2 e^(2x) (1/x - 1/(2x^2))*dx

Miscellaneous Exercise 6 | Q 4.06 | Page 150

Solve the following : int_4^9 (1)/sqrt(x)*dx

Miscellaneous Exercise 6 | Q 4.07 | Page 150

Solve the following : int_(-2)^3 (1)/(x + 5)*dx

Miscellaneous Exercise 6 | Q 4.08 | Page 150

Solve the following : int_2^3 x/(x^2 - 1)*dx

Miscellaneous Exercise 6 | Q 4.09 | Page 150

Solve the following : int_0^1 (x^2 + 3x + 2)/sqrt(x)*dx

Miscellaneous Exercise 6 | Q 4.1 | Page 150

Solve the following : int_3^5 dx/(sqrt(x + 4) + sqrt(x - 2)

Miscellaneous Exercise 6 | Q 4.11 | Page 150

Solve the following : int_2^3 x/(x^2 + 1)*dx

Miscellaneous Exercise 6 | Q 4.12 | Page 150

Solve the following : int_1^2 x^2*dx

Miscellaneous Exercise 6 | Q 4.13 | Page 150

Solve the following : int_(-4)^(-1) (1)/x*dx

Miscellaneous Exercise 6 | Q 4.14 | Page 150

Solve the following : int_0^1 (1)/(sqrt(1 + x) + sqrt(x))*dx

Miscellaneous Exercise 6 | Q 4.15 | Page 150

Solve the following : int_0^4 (1)/sqrt(x^2 + 2x + 3)*dx

Miscellaneous Exercise 6 | Q 4.16 | Page 150

Solve the following : int_2^4 x/(x^2 + 1)*dx

Miscellaneous Exercise 6 | Q 4.17 | Page 150

Solve the following : int_0^1 (1)/(2x - 3)*dx

Miscellaneous Exercise 6 | Q 4.18 | Page 150

Solve the following : int_1^2 (5x^2)/(x^2 + 4x + 3)*dx

Miscellaneous Exercise 6 | Q 4.19 | Page 150

Solve the following : int_1^2 dx/(x(1 + logx)^2

Miscellaneous Exercise 6 | Q 4.2 | Page 150

Solve the following : int_0^9 (1)/(1 + sqrt(x))*dx

## Chapter 6: Definite Integration

Exercise 6.1Exercise 6.2Miscellaneous Exercise 6

## Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 6 - Definite Integration

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Concepts covered in Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 6 Definite Integration are Fundamental Theorem of Integral Calculus, Properties of Definite Integrals.

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