Thank you for registering.

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

Please check your email for login details.
Close

MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

⇐ BackProceed to Checkout ⇒
There are no items in this cart.
Continue Shopping
Grade: 12th pass 

                        
Integration of (1+x-2x 2 ) 1/2 dx Integration of sininversex/(1-x 2 ) 3/2

							
    	
  1. Integration of (1+x-2x2)1/2dx
    2. 	
  2. Integration of sininversex/(1-x2)3/2
2 years ago

Answers : (2)

Susmita
425 Points 
							
Look at the denominator term within root.Try to write it as two whole square terms.
1+x-2x2
=1-2(x2-x/2)
=1-2(x^2-2.x.\frac{1}{4}+\frac{1}{16})+\frac{1}{8}
=\frac{9}{8}-2(x-\frac{1}{4})^2
=2[(\frac{3}{4})^2-(x-\frac{1}{4})^2]
So the integration becomes
\frac{1}{2}\int \frac{dx}{\sqrt{(3/4)^2-(x-1/4)^2}}
=\frac{1}{\sqrt{2}}sin^-1\frac{x-1/4}{3/4}
 
 
2 years ago
Susmita
425 Points 
							
In the 2nd integration put
z=sin-1x
So, dz=\frac{dx}{\sqrt{1-x^2}}
Also x=sinz
put these values in the integration.It will become
\int\frac{zdz}{cos^2z}
=\int\ z sec^2z dz
Now do integration by parts.Take z as 1st function.
\int\ z sec^2z dz
 
=ztanz-\int tanz dz
=ztanz+logcoz
=\frac{xsin^-1x}{\sqrt{1-x^2}}+log\sqrt{1-x^2}
Please approve the answer if it helps you.
2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Other Related Questions on Integral Calculus

wvacescqwacswvacescqwacswvacescqwacswvacescqwacswvacescqwacswvacescqwacswvacescqwacswvacescqwacswvac... Answer & Earn Cool Goodies
{ ( cos ^-1x { √(1-x^2) }]^-1) ÷ ( log e { 1 + ( sin(2x√(1-x^2)) ÷ 2) }) dx Answer & Earn Cool Goodies
integrate the following ∫dx/(5 +7 cos x+sin x) the answer is 1/5 log|tan x/2+2|/|tan x/2-2| + c but...
In this particular question how would we think that we have to put t=tan(x/2)????
This is a type of integral x f(x) . But I am unable to solve it. Ans: Option 2
View all Questions »


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