Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
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
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Evaluate: `int 1/(x(x-1)) dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
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:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x:
`(10x^9 10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t. x : `(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate: ∫ |x| dx if x < 0
`int sqrt(1 + sin2x) "d"x`
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int x^x (1 + logx) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int (logx)^2/x dx` = ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate `int1/(x(x - 1))dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` 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).
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).