Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `int cos^2x.dx`
Advertisements
उत्तर
Recall the identity cos 2x = 2 cos2x – 1, which gives
`cos^2x = (1 + cos2x)/(2)`
Therefore, `int cos^2 x.dx`
= `(1)/(2)int (1 + cos 2x).dx`
= `(1)/(2)int dx + (1)/(2) int cos 2x .dx`
= `x/(2) + (1)/(4)sin 2x + C`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
`int (cos2x)/(sin^2x) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int1/(4 + 3cos^2x)dx` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
