English

Find: ∫ Sin X · Log Cos X Dx - Mathematics

Advertisements
Advertisements

Question

Find: ∫ sin x · log cos x dx

Sum

Solution

`∫  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

shaalaa.com
  Is there an error in this question or solution?
2018-2019 (March) 65/1/3

RELATED QUESTIONS

 

If `sin (sin^(−1)(1/5)+cos^(−1) x)=1`, then find the value of x.

 

Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=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)  x/(sqrt(a^2 - x^2))`, |x| < a


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`


if `tan^(-1)  (x-1)/(x - 2) + tan^(-1)  (x + 1)/(x + 2) = pi/4` then find the value of x.


Solve  `tan^(-1) -  tan^(-1)  (x - y)/(x+y)` is equal to

(A) `pi/2`

(B). `pi/3` 

(C) `pi/4` 

(D) `(-3pi)/4`


Prove that

\[2 \tan^{- 1} \left( \frac{1}{5} \right) + \sec^{- 1} \left( \frac{5\sqrt{2}}{7} \right) + 2 \tan^{- 1} \left( \frac{1}{8} \right) = \frac{\pi}{4}\] .

 

Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .


Solve: tan-1 4 x + tan-1 6x `= π/(4)`.


Find the value of  `tan(sin^-1  3/5 + cot^-1  3/2)`


Solve: `sin^-1  5/x + sin^-1  12/x = pi/2`


Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`


Choose the correct alternative:

`sin^-1 (tan  pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation


Prove that cot–17 + cot–18 + cot–118 = cot–13


Show that `2tan^-1 {tan  alpha/2 * tan(pi/4 - beta/2)} = tan^-1  (sin alpha cos beta)/(cosalpha + sinbeta)`


If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.


If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.


If cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β(γ + α) + γ(α + β) equals ______.


sin (tan−1 x), where |x| < 1, is equal to:


If `"tan"^-1 2  "x + tan"^-1 3  "x" = pi/4`, then x is ____________.


`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.


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 ____________.


Solve for x : `{"x cos" ("cot"^-1 "x") + "sin" ("cot"^-1 "x")}^2` = `51/50


The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:

Measure of ∠EAB = ________.


The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:

Domain and Range of tan-1 x = ________.


Find the value of `sin^-1 [sin((13π)/7)]`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×