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.
MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

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

                        

Find the value of the Integral -p/2 to p/2 v(cos x-cos ³x)dx

6 years ago

Answers : (2)

Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points
							
212-1130_Untitled.png



6 years ago
Bhanutej Prabhakar Ravilla
23 Points
							taking cos x common from the term in the brackets the given integral sum is simplified to 
integral (vcosx).sinx dx
substitute cosx = t(say)
then -sinx.dx=dt
the integral again becomes :
integral(-pi/2 to pi/2) of -(vt).dt
now  we observe that the function root(cosx-cosx^3) is an even function as changing the variable x to its negative (-x) dosnt change the equation.
so integral(-pi/2 to pi/2 ) becomes:
2*integral(0 to pi/2)-(vt).dt
but wen x=0 cosx in 1. and wen x=pi/2 ,cosx is 0. so the integral again becomes:
2*integral(1 to 0) -(vt).dt
now interchange the limts of the integral and take out the negative sign.the integral now is:

2*integral(0 to one)(vt).dt   which is simply:
2*(2/3)*(t^3/2) from 0 to 1
which is -------->>>4/3.
						
6 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
Vouchers
To Win!!! Click Here for details