Find the integrals of the following: 14-x2

Find the integrals of the following:

`1/(4 - x^2)`

Sum

`int 1/(4 - x^2) "d"x = int 1/((2)^2 - (x)^2) "d"x`

`int 1/("a"^2 - x^2) "d"x = 1/(2"a") log|("a" + x)/("a" - x)| + "c"`

`int 1/(4 - x^2) "d"x = 1/(2(2)) log |(2 + x)/(2 - x)| + "c"`

= `1/4 log |(2 + x)/(2 - x)| + "c"`

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Chapter 11: Integral Calculus - Exercise 11.10 [Page 219]

Chapter 11 Integral Calculus
Exercise 11.10 | Q 1. (i) | Page 219

Find the volume of solid generated by rotating the area bounded by x²+y² =36 and the lines x = 0, x = 3 about X -axis.

Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.

Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx

Integrate the following functions with respect to x :

`1/((x - 1)(x + 2)^2`

Integrate the following with respect to x :

`x/sqrt(1 + x^2)`

Integrate the following with respect to x :

`("e"^x - "e"^-x)/("e"^x + "e"^-x)`

Integrate the following with respect to x :

`cot x/(log(sin x))`

Integrate the following with respect to x :

x(1 – x)¹⁷

Integrate the following with respect to x:

x³ sin x

Integrate the following with respect to x:

`"e"^x (tan x + log sec x)`

Find the integrals of the following:

`1/((x + 1)^2 - 25)`

Find the integrals of the following:

`1/sqrt((2 + x)^2 - 1)`

Find the integrals of the following:

`1/sqrt(x^2 - 4x + 5)`

Find the integrals of the following:

`1/sqrt(9 + 8x - x^2)`