Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Advertisements
उत्तर
`intsqrt(1 - cos 2x)dx`
= `intsqrt(2sin^2x)dx`
= `sqrt(2) int sin x dx`
= `-sqrt(2)cos x + c`.
APPEARS IN
संबंधित प्रश्न
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
cot x log sin x
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int cos^7 x "d"x`
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int 1/(x(x-1))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If \[x=g(t)\] and \[dx=g'(t)dt\], which formula represents integration by substitution?
What is \[\int\cot t\,dt\] in the evaluation of \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
