The value of ∫0π4tanxdx + ∫0π4cotxdx

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

21.

What is the solution of the differential equation

logdydx - a = 0

  • y = xea + c

  • x = yea + c

  • y = lnx + c

  • x = lny + c


22.

e - 1e - 2logxxdx = ?

  • 32

  • 52

  • 3

  • 4


23.

What is tan-1secx + tanxdx = ?

  • πx4 +x24 +c

  • πx2 + x24 + c

  • πx4 +πx24 + c

  • πx4 - x24 + c


24.

What is 02π1 + sinx2dx = ?

  • 8

  • 4

  • 2

  • 0


Advertisement
25.

lnx - 1dx - lnx - 2dx = ?

  • xlnx  - 1 + c

  • xlnx - 2 = c

  • xlnx + c

  • xlnx2 + c


Advertisement

26.

The value of 0π4tanxdx + 0π4cotxdx = ?

  • π4

  • π2

  • π22

  • π2


D.

π2

0π4tanxdx +0π4cotxdx = 0π4tanx + cottxdx= 0π4 sinx + cosxsinxcosxdx = 20π4sinx + cosx1 - sinx - cosx2dxPutting sinx - cosx = t dt = sinx + cosxdxwhen x = 0, t = - 1 and x = π4, t = 0= 2 - 1011 - t2dt = 2 - 10sin-1t - 10= 20 -  - π/2= π2


Advertisement
27.

Consider the functions

f(x) = xg(x) and g(x) = 1x

where [ . ] is the greatest integer function

  • 16

  • 13

  • 518

  • 536


28.

Consider the functions

f(x) = xg(x) and g(x) = 1x

where [ . ] is the greatest integer function

What is 131fxdx

  • 3772

  • 23

  • 1772

  • 37144


Advertisement
29.

Given that

an = 0πsinn + 1xsin2xdx

Consider the following statements :

  1. The sequence {a2n } is in AP with common difference zero.
  2. The sequence {a2n + 1} is in AP with common difference zero.

Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • both 1 and 2

  • neither 1 nor 2


30.

Given that

an = 0πsinn + 1xsin2xdx

What is an - 1 - an - 4 = ?

 

  •  - 1

  • 0

  • 1

  • 2


Advertisement