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(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`x/(9 - 4x^2)`
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
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following : `int sinx/(sin 3x).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int cot^2x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
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.
`int 1/(x^2 + 4x - 5)dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
