Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
उत्तर
Let I = `int "x" sqrt(1 + "x"^2)` dx
Put 1 + x2 = t
∴ 2x . dx = dt
∴ x . dx = `1/2` dt
∴ I = `1/2 int sqrt"t" * "dt"`
`= 1/2 int "t"^(1/2) *` dt
`= 1/2 * "t"^(3/2)/(3/2)` + c
`= 1/3 "t"^(3/2)` + c
∴ I = `1/3 (1 + "x"^2)^(3/2)` + c
APPEARS IN
संबंधित प्रश्न
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int x^3"e"^(x^2) "d"x`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int 1/(x(x-1)) dx`
