Balbharati solutions for मैथमेटिक्स एण्ड स्टैटिस्टिक्स १ (कॉमर्स) [अंग्रेजी] कक्षा १२ महाराष्ट्र स्टेट बोर्ड chapter 6 - Definite Integration [Latest edition]

Evaluate the following definite integral:

`int_4^9 (1)/sqrt(x)*dx`

Evaluate the following definite integral:

`int_(-2)^3 (1)/(x + 5)*dx`

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

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

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

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

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

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

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

Evaluate the following definite integral:

`int_1^2 (3x)/((9x^2 - 1))*dx`

Evaluate the following definite integral:

`int_1^3 logx.dx`

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

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

Evaluate the following integrals:

`int_1^3 (root(3)(x + 5))/(root(3)(x + 5) + root(3)(9 - x))*dx`

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

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

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

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

Evaluate the following integral:

`int_0^1 x(1 - x)^5 *dx`

Choose the correct alternative :

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

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

Choose the correct alternative :

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

Choose the correct alternative : 

`int_4^9 dx/sqrt(x)` =

Choose the correct alternative :

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

Choose the correct alternative :

`int_2^3 x^4*dx` =

Choose the correct alternative :

`int_0^2 e^x*dx` =

Choose the correct alternative :

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

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

Choose the correct alternative :

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solve the following:

`int_1^3 x^2 log x*dx`

Solve the following:

`int_0^1 e^(x^2)*x^3dx`

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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