Advertisements
Advertisements
प्रश्न
Find: ∫ sin x · log cos x dx
उत्तर
`∫ sin "x" ·log cos"x" "dx"`
Substitute cos x = t
sinx dx = dt
`∫ - "log t dt"`
= - (t log t - t ) + C
= - t log t + t + C
= - cos x log (cos x )+ cos x + C
APPEARS IN
संबंधित प्रश्न
Prove that `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2;x in (0,pi/4) `
Write the following function in the simplest form:
`tan^(-1) (sqrt(1+x^2) -1)/x, x != 0`
Write the following function in the simplest form:
`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt3 <= x a/sqrt3`
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Find the value of `cot(tan^(-1) a + cot^(-1) a)`
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
`cos^(-1) (cos (7pi)/6)` is equal to ______.
Prove that:
`sin^(-1) 8/17 + sin^(-1) 3/5 = tan^(-1) 77/36`
Prove that:
`cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`
Solve the following equation:
`2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)`
Solve for x : \[\tan^{- 1} \left( \frac{x - 2}{x - 1} \right) + \tan^{- 1} \left( \frac{x + 2}{x + 1} \right) = \frac{\pi}{4}\] .
If cos-1 x + cos -1 y + cos -1 z = π , prove that x2 + y2 + z2 + 2xyz = 1.
Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec" x)`
Choose the correct alternative:
`tan^-1 (1/4) + tan^-1 (2/9)` is equal to
Choose the correct alternative:
If |x| ≤ 1, then `2tan^-1x - sin^-1 (2x)/(1 + x^2)` is equal to
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
Prove that `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/((1 + x^2) - sqrt(1 - x^2))) = pi/2 + 1/2 cos^-1x^2`
If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of `"sec" theta + "tan" theta` is ____________.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
The domain of the function defind by f(x) `= "sin"^-1 sqrt("x" - 1)` is ____________.
The value of expression 2 `"sec"^-1 2 + "sin"^-1 (1/2)`
`"cot" ("cosec"^-1 5/3 + "tan"^-1 2/3) =` ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 + "tan"^-1 1/8 =` ____________.
`"tan"^-1 (sqrt3)`
`"sin"^-1 ((-1)/2)`
If `3 "sin"^-1 ((2"x")/(1 + "x"^2)) - 4 "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x is equal to ____________.
What is the value of cos (sec–1x + cosec–1x), |x| ≥ 1
`"tan" ^-1 sqrt3 - "cot"^-1 (- sqrt3)` is equal to ______.