Advertisements
Advertisements
Question
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Advertisements
Solution
`intsqrt(1 - cos 2x)dx`
= `intsqrt(2sin^2x)dx`
= `sqrt(2) int sin x dx`
= `-sqrt(2)cos x + c`.
APPEARS IN
RELATED QUESTIONS
Find `intsqrtx/sqrt(a^3-x^3)dx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`(1+ log x)^2/x`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following : `int (logx)2.dx`
`int logx/(log ex)^2*dx` = ______.
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int sqrt(1 + sin2x) dx`
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Which substitution is appropriate for \[\sqrt{\frac{x}{a-x}}\], \[\sqrt{\frac{a-x}{x}}\], \[\sqrt{x(a-x)}\], or \[\frac{1}{\sqrt{x(a-x)}}\]?
What is the value of \[\int\sin^3x\cos^2x\,dx\]?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
