badge image

Enroll For Free Now & Improve Your Performance.

User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.

Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping
Grade: 12


1.∫(Sin 4 x/Cos 2 x).dx=? 2.∫{1+sin(x/2)} 1/2 dx=? Please give elaborate answers for these at the earliest...

9 years ago

Answers : (2)

vikas askiitian expert
509 Points

I = (sinx/2 + 1)1/2 dx

(sinx/2+1) = (sinx/4)2 + (cosx/4)2 + 2cosx/4sinx/4   =  (sinx/4 + cosx/4)2

after putting this

I ={ sinx/4 + cosx/4 }dx

I= -4cosx/4 + 4sinx/4 + c

please approve my ans if u like it

9 years ago
Aman Bansal
592 Points

dear chilukuri,


Possible intermediate steps:
integral sec(2 x) sin(4 x) dx
Simplify the integrand sin(4 x) sec(2 x) to get 4 sin(x) cos(x):
= integral 4 sin(x) cos(x) dx
Factor out constants:
= 4 integral sin(x) cos(x) dx
For the integrand sin(x) cos(x), substitute u = cos(x) and du = -sin(x) dx:
= -4 integral u du
The integral of u is u^2/2:
= -2 u^2+constant
Substitute back for u = cos(x):
= -2 cos^2(x)+constant

2.∫{1+sin(x/2)}1/2 dx

(4*(-Cos[x/4] + Sin[x/4])*Sqrt[1 + Sin[x/2]])/ (Cos[x/4] + Sin[x/4])

We are all IITians and here to help you in your IIT JEE preparation.

Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar.. 



9 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Course Features

  • 51 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details