0

Guest

Courses New

Please solve this............. the correct answer is pi/8. Question is attatched.

Please solve this............. the correct answer is pi/8.
Question is attatched.

Question Image
Grade:12

1 Answers

Aditya Gupta
2081 Points
4 years ago
this ques is an application of the property that integral of f(x) from a to b is equal to integral of f(a+b – x) from a to b.
so let I= int 0_pi/2 s^3*c/(s^4+c^4) dx where s= sinx and c=cosx
now I= int 0_pi/2 c^3*s/(c^4+s^4) dx where we have replaced x by 0+pi/2 – x
now add the two eqns
2I= int 0_pi/2 sc*(s^2+c^2)/(s^4+c^4) dx=int 0_pi/2 sc/(s^4+c^4) dx
now put y=s so that dy= c dx
2I= int 0_1 y/(y^4+(1 – y^2)^2) dy
now put y^2= z so that 2ydy= dz
hence 4I= int 0_1 dz/(z^2+(1 – z)^2) dz=  int 0_1 dz/(2z^2 – 2z+1) dz
now solving this is beyond easy as this is a standard form (1/quadratic). so you can do it to get the final answer as pi/8

Think You Can Provide A Better Answer ?

Other Related Questions on Vectors

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More