Question: Evaluate : ∫1-cos 6xdx, where x ∈ (0, π6)


A ) 23cos x + C
B ) - 23cos 3x + C
C ) 23cos 3x + C
D ) 22cos x + C

Steps to derive

1 ∫1-cos 6xdx=∫2sin23xdx
 [Use 1 - cos 2x = 2sin2x.]

2 = ∫2sin 3xdx
 [3x ∈ (0, π2).]

3 = (2)∫sin 3xdx

4 = (23)(-cos 3x) + C

5 = - 23cos 3x + C



Hence the right answer is Option B

Click Here To Go Back


Explore Related Questions

  • choose f ′ (x) from the following if x = cos28xcos 28x..
  • If f (x) = 1- tan 2x1 + tan 2x, then choose f ′ (x) from th..
  • If f (x) = 1 + cot 3x1- cot 3x, then find f ′ (x)...
  • Find the derivative of sin x...
  • Which of the following is the derivative of cos x?..
  • Find the derivative of tan x...
  • Find the derivative of cot x...
  • Find the derivative of sec x...
  • Find the derivative of cosec x...
  • Find the derivative of e2x...
  • An enemy war ship was traced on a radar sheet. The course of that ship was identified as 5..
  • There are two examination halls P and Q. If 60 students are sent from P to Q then the numb..
  • Nathan is driving to his office. The graph shows the path he takes. This path is modeled b..
  • Evaluate: 30+30+30+.......∞..
  • Evaluate: 999..........∞..
  • If A = (434- 342) and B = (4- 41342) then find the determinant of AB...
  • Find the sum of the infinite geometric series.55+1+55+5+555+5+......
  • If f (z) = z + 8, g (z) = z2, then for what value of z, f [g(z)] = g [f(z)]...
  • If f(z) = 1- z1+ z then find f o f o f o f o f o f (8192)...
  • Evaluate: 12 - 22 + 32 - 42 + 52 - 62 + ...........+ 20012 - 20022 + 20032..
  • Factor: a(a - 8) - b(b - 8)..
  • Evaluate : ∫(x2+x3)dx..
  • Evaluate : ∫x15(7+x18)2dx..
  • Evaluate : ∫1x15(x-1x)(x10+1x10)dx..
  • Evaluate : ∫(5+x)(16x-5)x16dx..
  • Evaluate : ∫1-cos 6xdx, where x ∈ (- π6, 0)...
  • Evaluate : ∫tan-11-cos 14x1+cos 14xdx, where x ∈ (0, π2)...
  • Evaluate : ∫cos2 43x1-sin  43xdx..
  • Evaluate : ∫11+sin 5x dx..
  • Evaluate : ∫cosec 4xcosec 4x-cot 4x dx..
  • Three cyclists P, Q and R with the same speed starts from A to reach E as shown in the fig..
  • Evaluate : ∫sin2 7xsec2 7xdx..
  • Evaluate : ∫1+cos 6xdx, where x ∈ (0,π2)...
  • Evaluate : ∫1+cos 2xdx, where x ∈ (π2, π)...
  • Find the sum of oranges shown by the varieties Valencia and Tangerine, from the table...
  • Evaluate : ∫sin23x1+cos 3x dx..
  • Evaluate : ∫11-sin 4x dx..
  • Evaluate : ∫11+cos 2x dx..
  • Evaluate : ∫11-cos 2x dx..
  • Evaluate : ∫sec 2xsec 2x+tan 2x dx..
  • Evaluate : ∫cos25x.cosec25x dx..
  • Evaluate : ∫sec24x.cosec24xdx..
  • Evaluate : ∫cot- 11-cos 10x1+cos 10xdx..
  • Evaluate : ∫e-logecosec 7xdx..
  • Evaluate : ∫e2logecot 3xdx..
  • Evaluate : ∫42log4 sec 9xdx..
  • Evaluate : ∫e4loge xdx..
  • Evaluate : 17(∫8-log64x2dx)..
  • Evaluate : ∫a4x+10dx..
  • Evaluate : ∫e-loge sec 35xdx..